Q:

Does friction always oppose motion?

Recently I had the following misconceptions: 

Static friction always opposes the motion of body.
The force of friction cannot initiate motion in a body.

Now I came to know that my understanding was wrong and that friction indeed can cause motion in bodies, and that static friction does not always oppose the motion of a body.
But I found this quite bizarre, how can a force which has always been taught to us to oppose motion, oppose points 1. and 2.?

A:

Friction opposes relative motion between two bodies. 
Note that might mean that friction can create motion relative to i.e. you. For example, dropping an item on a moving belt. Friction opposes and reduces the relative motion of the item and belt until they move together. But now they’ve started moving relative to you. 

A:

Friction opposes the motion between THE TWO SURFACES IN CONTACT (the motion that would have happened if there was no friction). You can walk because the friction pushes the sole of your shoe forward. If there was no friction, the sole of the shoe would move backward (the direction you are kicking the Earth).
Whether those surfaces are in moving/rotating parts of a composite object is another story. Again, it is not about the relative motion of the bodies, but about the motion of the surfaces in contact. When the tires in your car are rotating, the point of contact of the tires against the road is pushing the road towards the back of the car. Without friction, the tires would spin in the same place. Because of friction, the tires push the road backward and, by the 3rd law, the road pushes the tires forward. That happens when you are speeding up. When you are slowing down, the point of contact of the tires with the road begin to push the road forward. Note that the car is still moving forward. That proves it is not about the relative motion of the bodies but about the motion of the surfaces (that would have happened if there was no friction). Ergo, the other answer is incorrect.

This is very interesting. The moderators erased some of my comments where my rudeness was on full display. Since my comments were correct from the science point of view (maybe not politically correct), I am going to double down.
One of my finest moments was on my reply to "Friction between a moving car and the road will only ever slow down the car (relative to the road), it will never increase their relative velocity." I suggested that if the author of such blasphemy truly believed that being true, then he/she/it should drive to the middle of a frozen lake, change the tires for some worn out ones, maybe douse some water around the tires to make the ice smother, and try to drive out of the lake. All hail darwinism. The exchange might have harmed some sensibilities, but the message was clear and correct. I hope he/she/it learned some Physics as Dude156 did on another of my answers. 
There was another fine comment mentioning that the most voted answer could be savaged by subdividing the bodies into the parts that are in contact and the rest of body. In particular, that post mentioned that tires have a so-called contact patch. Thus, friction opposes the relative motion of the contact patch of the tire and the road. I replied that such a point of view is less optimal than mentioning that friction opposes the motion between the surfaces from the very beginning.
See you at physicsoverflow. Peace out. 

A:

The top answer given is correct, but I wanted to slightly extend this:

how can a force which has always been taught to us to oppose motion, oppose points 1) and 2)?

Imagine a table, I slide a very heavy hockey puck over the table. Without friction, the puck keeps sliding. But because there is friction, the puck is slowed down.
Now let's put the table on wheels and do the same test again. Without friction, the table does not move and the puck slides right off. BUT with friction, the friction takes the kinetic energy of the puck and imparts it to the table. Because of this (and because we put the table on wheels), the table now starts moving forward.
Because there is friction, the kinetic energy is transferred from the puck to the table, which can cause the table to start moving (given the right circumstances whereby the energy imparted to the table overcomes the table's own friction with whatever it's resting on).

There are common real world examples here, e.g. someone who takes a running jump, and lands on a stationary carpet/skateboard, which then starts moving because the friction keeps the carpet/skateboard and the person's feet together and therefore the person's kinetic energy is (partially) transferred to the carpet/skateboard.

