A pitcher is only allowed to go to his mouth in certain circumstances, usually when it is very cold.
The pitcher shall not_ (a) (1) Bring his pitching hand in contact with his mouth or lips while in the 18 foot circle surrounding the pitching rubber. EXCEPTION: Provided it is agreed to by both managers, the umpire prior to the start of a game played in cold weather, may permit the pitcher to blow on his hand. PENALTY: For violation of this part of this rule the umpires shall immediately call a ball. However, if the pitch is made and a batter reaches first base on a hit, an error, a hit batsman or otherwise, and no other runner is put out before advancing at least one base, the play shall proceed without reference to the violation. Repeated offenders shall be subject to a fine by the league president
Going to your mouth is an opportunity to put a foreign substance (even spit) on to your hand and then on the ball that could alter the tragectory of the ball in flight.