This may have been brought up before but here it goes anyways.
Play. Center snaps the ball, lineman reaches out and grabs the back of the defensive linemans head (not the edge) and pulls/pushes him to the ground by the head.

Illegal block? And if not why?

I say it is illegal as rule 2-3 says the block must be from the shoulders down, but we have others around here that says it is not.

This is not a Illegal block. It is a foul however for Illegal use of the hands (9-2). The blockers hands are outside of the player being blocked “frame of the body”. He has also initiated contact with an opponent above the shoulders (see 2-3-3).

What about if the defense was doing this to the offense?

A defensive player with a few minor differences must comply with the same rules as a offensive player. The big thing to me is the contact above the shoulders. Per 2-3 that is not allowed by players on either team.