Ah hahah.
So that's what that code does....
Hypothesis:
That code makes him stop from going into a wall on the left side.
The movement skipping only happens when he's moving left at half max speed.
Half max speed means he'll still go over the tile, but he drops ever slightly mid-gap.
Lets say he is moving left at half speed. He drops a few pixels into the gap but he's still moving fast enough to the left. Then collision happens, but another piece of code sees that he's not low enough so he can still go on top. Therefore the other piece of code hoists him up back on top, while the left collision block code still activated, saying he should stop at the block edge. But cause his position was hoisted up, it snaps him to the opposite edge.
That's my hypothesis why the snapping doesn't occur when you disable the left blocking code.