I think it's to avoid a situation where a player does a move, sees how his opponent reacts, realizes his mistake and retracts his move - leading to argument, or players having to control their reactions until they're really really sure their opponent finished his move, etc. Chess is supposed to be about strategy, not about bickering about whether a move was really confirmed and trying to guess which move is good by watching your opponent's face.

Also, it's to force new players to think quietly, which is good for them anyway in the long run.

I don't know about its history, but I imagine that the point is to discourage grabbing a piece and hovering it over where you are thinking of moving it to visualize better the new situation that would arise. Doing this seems to violate the spirit of the game if you think an important part of it is to be able to look ahead and calculate in your mind's eye. Plus it could be annoying/distracting for the opponent.