Q:

Why are only some predestined?

Specifically with respect to the Westminster Confession of Faith (1646)...
Chapter 3, paragraph 3 and 4, where it states:

III. By the decree of God, for the manifestation of His glory, some men and
      angels are predestinated unto everlasting life; and others foreordained to
      everlasting death.
IV. These angels and men, thus predestinated, and foreordained, are
      particularly and unchangeably designed, and their number so certain and
      definite, that it cannot be either increased or diminished.

Why or how would they justify that by using the scriptures? Having justified that, why are only some people predestined for certain salvation and some others for certain damnation, with presumably the rest being left for fate or whatever choice those people decide to make (A concession for Arminianism)?

A:

Note that this response has been divided into two parts: the first is the original response, and the second tries to elaborate based on a comment from the OP.
Part 1
Great question. This response includes a very brief description of some of the basic points of predestination/election, and some references with in-depth, historic information.

Here are a few main points of predestination/election, which it sounds like you may already be aware of. Again, these points are part of Reformed/"Calvinist" theology, and there are many that would disagree.

Reformed theology emphasizes God's motivation to glorify himself, to "bring glory to his name." Note that, according to reformed theology, this does not make him selfish, because man was designed and created to worship God, so glorifying God is what is best for man. (See John Piper, & what is sometimes called "Christian Hedonism." Resources at DesigingGod.org).
All are considered guilty in Adam, and therefore "deserve" the torment of hell (see the doctrine of "original sin").
Because God is sovereign, he does not "owe" salvation to anyone, and would be justified in sending all of humanity to hell.
God is glorified in the greatness of his mercy by electing some to salvation, which they cannot earn.
God is glorified in the greatness of his wrath, by sending others to hell -- either those who are "not elect" or who are "elected to damnation" (see the doctrine of "double predestination").

Again, from the perspective of reformed theology, it is important to note that those who are predestined for salvation are in no way "deserving" of God's mercy, and there is no way to "earn" or "merit" redemption. (See the doctrines of "monergistic" vs "synergistic" regeneration).
How God has decided specifically which individuals will go to heaven is explained either as "random" or as one of the "mysteries" not revealed to man.

Some brief history and additional reference material. Your question is about the Westminster Confession and what it says about predestination; the Confession was published in 1646, but the question of predestination had been ongoing for sometime. One important document where it is addressed directly is the Canons of Dordt (sometimes "Dort"). Several followers of Arminius published a "Remonstrance" in 1610 in Holland, refuting some elements of reformed doctrine, and the Synod of Dordt was created to respond to their assertions. The Synod published their conclusions in a document called the Canons of Dordt in 1618. It is generally considered the source of the "five points of Calvinism," or "T.U.L.I.P." -- Calvin himself never actually outlined the five points in that form -- and addresses predestination in some detail, with scripture proofs. Here are two links to the Canons of Dordt, with scripture proofs: Reformed.org; CCEL. See here for a quick explanation of the history of the five points of Calvinism.
As to your question about "[w]hy or how would they justify that by using the scriptures,"
the Westminster Assembly included extensive scripture proofs that, in their interpretation, justified all of the statements in the Standards. A full copy of the Confession, with the original proofs, can be found on the Reformed.org page linked in your question.
Note also that you can find an in-depth, detailed discussion of the creation of the Westminster Standards in the History of the Westminster Assembly of Divines, published in 1853 by William Maxwell Hetherington.
There is also a very detailed chapter on the Westminster Standards in Philip Schaff's "Creeds of Christendom," published 1876.
Schaff's Creeds is a widely regarded, historically important book, one that is likely to be found on the bookshelves of many historians and theologians. Hetherington's work is new to me, but I see that it is linked alongside other important historical titles by sources I have found to be credible.

Part 2
In the OP's comment on 'Part 1' of this response, he gives an analogy to further clarify the question, which I'll paraphrase here: 'if, for example, 1/3 of the people on earth are predestined for heaven, why are the other 2/3 not predestined?' I've added this "Part 2" in an attempt to better address the question.
As a preface, please note that I don't claim to be an expert on predestination, but I'll try to share what I've learned.
There is what could be described as a 'subtle' difference in two basic forms of the doctrine of predestination, with the variant being described as 'double predestination,' or 'reprobation.' This doctrine says that God has predestined some to go to heaven, and others to go to hell, and that all people are predestined for one or the other. Another version is that God has predestined some to go to heaven, and has simply "passed over" the others, leaving them to be condemned by their own guilt, which they inherited from Adam and compounded through their own actions, since "all have sinned" (Rom 3:23). The end result is the same, from the perspective of the individuals and where they spend eternity; anyone who is not elected to salvation doesn't make it to heaven, according to the doctrine of predestination. Also, note that in neither case is there a "third category." In predestination, every person is either elected to salvation, or "passed over." In double predestination, every person is elected to either salvation or reprobation. Here's a work from John Bunyan that examines the doctrine of reprobation in detail.
I realize that you've stated that your question is not about predestination, but, since these matters are all intertwined, a thorough understanding of it may help to resolve your question. This C.SE post by Caleb does a great job of explaining things, and I think it's relevant to our discussion here. He also does a good job of explaining the role of substitutionary atonement, in a very concise manner -- that is, how God can offer salvation to guilty sinners who are deserving of punishment, without being unjust, although you may already understand all of that.
The question of why God has chosen a certain number of people to be saved is a matter of his sovereign will. Since he doesn't owe salvation to anyone, and no one besides Christ is capable of "earning" salvation, God can choose to have mercy on as many or as few as he chooses -- it's a free gift that he is not required to offer. An interesting reference here is Matthew 7:13-14, which tells us that "many" [ESV] will go to hell, and "few" will go to heaven, although I haven't checked the original languages on that verse. OTOMH, that's the only reference that I know of that suggests the numbers/ratios involved in who will go to heaven and who won't, although I expect there are likely references to be found in Revelation.
You might enjoy a read of Romans 9, esp. v. 19-29, and Romans 8:29.
I suppose God could have chosen to apply Christ's atonement to everyone. (Edit: See 1 Tim 2:3, a verse sometimes seen as complicating defenses of predestination). No doctrinal references that discuss the matter come to mind, and I generally seek to avoid providing my own exposition. I do know that there is nothing that would obligate him to apply Christ's atonement to all people, and that the consistent teaching is that God did not create sin, and that he remains perfectly holy and free of all guilt in choosing to bar unforgiven sinners from his paradise. Christ's atonement is sometimes described as being "sufficient" for all, but "efficient" only for the elect -- so, the infinite merit of Christ's sacrifice means that God could justly elect to salvation as many as he willed, and he chose to save a certain number, which is not disclosed to us.
This might seem to conflict with many people's understanding of God's character. It is important to remember that Reformed theology, in an effort to accurately reflect the teachings of the bible, emphasizes God's sovereignty, as well as his motivation to glorify himself.

I hope this response doesn't seem unnecessarily complicated; your question, as I understand it, seems fairly simple at first, but it actually addresses some very contentious areas of theology that have been debated for centuries. Countless sermons, treatises, and expositions have been written on the matter. I encourage you to consult some of the sources I've linked to, especially those in the second section of part 1; I'm sure they can explain things more clearly than I can, though I suppose I could still try to revise -- and hopefully shorten! -- this answer. Cheers.

A:

I found a great explanation by John Piper on why some people are "predestined" to hell:
https://soundcloud.com/askpastorjohn/god-glorified-predestination-hell
Summary
As preface to the question, he makes the following qualifying points:

Nobody is in hell that doesn't deserve to be there, and isn't in active rebellion to God. The idea that there could be someone who genuinely loves God and is still in hell is foreign to the Bible.
The Bible portrays God as saving sinners, not making good people to be really bad.

He then says, with those in mind, how is God glorified by creating a universe where, whether by his design or by his permission, people will end up in hell justly?

God's goal is that the full range of his perfections would be known, including his wrath and his power, as well as his love and his mercy. To do that, there is a dark backdrop of the fall of man, and grace shines more brightly because it's against the backdrop of sin.

As is common, the verse cited is Romans 9:22-23 (ESV):

22 What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, 23 in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory

A:

I don't think we're going to resolve the whole predestination vs freewill debate here, so I'm not going to go into the arguments for either side.
But let me try to clarify the debate. The whole idea of predestination is that God has determined in advance who will be saved and who will not. As Arafangion points out in his comment, a Calvinist would not say that someone who is predestined to be saved will therefore go to Heaven regardless of his beliefs and actions and vice versa. That is, Calvinists do not say that if God chooses Al and not Bob that that means that Al will be saved even if he rejects Christ and is a serial killer and a rapist, etc, etc, while Bob will be condemned even if he is the most holy person in the world. Rather the Calvinist says that God decides who will turn to him and who will not. Those whom God has chosen will accept Christ and try to serve him; those whom he has not chosen will reject Christ and have no desire to follow his commands. Thus, if you had some list of who is saved and who is not, and you compared this list to what you could observe about people's lives, this would give NO EVIDENCE one way or the other about whether predestination is true.
That said, the Calvinist would also say that it is not a matter of some are chosen to be saved, some to be condemned, and "the rest left to fate or whatever choice those people make". Rather, everybody is predestined either to be saved or to be condemned. There is no third category. Those who are predestined to be saved will accept Christ. Those who are predestined to be condemned will reject him. There is no third possibility: you do or you don't.
As to scriptural justifications, the most obvious is Epehesians 2:8, "For by grace you have been saved through faith, and that not of yourselves; it is the gift of God." Your faith is a "gift of God". The Calvinist says that God decides who will have faith and who will not. Or Romans 8:29-30, "For whom He foreknew, He also predestined to be conformed to the image of His Son, that He might be the firstborn among many brethren. Moreover whom He predestined, these He also called; whom He called, these He also justified; and whom He justified, these He also glorified." Again, God predestined certain people, these people he "called", and then they responded. 
A key scripture for Calvinists is Romans 9:10-21, "... But when Rebecca also had conceived by one man, even by our father Isaac (for the children not yet being born, nor having done any good or evil, that the purpose of God according to election might stand, not of works but of Him who calls), it was said to her, “The older shall serve the younger.” As it is written, “Jacob I have loved, but Esau I have hated.” What shall we say then? Is there unrighteousness with God? Certainly not! ... You will say to me then, “Why does He still find fault? For who has resisted His will?” But indeed, O man, who are you to reply against God? Will the thing formed say to him who formed it, “Why have you made me like this?” Does not the potter have power over the clay, from the same lump to make one vessel for honor and another for dishonor?"
If you're not a Calvinist -- or maybe even if you are -- this is a tough passage.

