Why can't baseball pitchers hit?

Probably for a similar reason why catchers can't pitch. They are used to doing one thing, and have probably catered their workouts off the field to augment their abilities. Not hard 2 figure out.

Because hitting is not what they are paid to do. They are sort of like speciailists, the practice only on their pitching and thus neglegtthe hitting portion of the game. In the American leauge its irerelevant because of the Designated Hitter rule, but in the NL pitchers and their inability to hit really affect strategy.

First, to even get a .250 average in the Majors requires tremendous skill. If we tried it we would probably be in the .050 range. So if pitchers are just ordinary batters, they aren't going to be very good.

Second, they only pitch every four or five days if they are a starter in the National League and so they don't get anywhere near the same amount of everyday game experience as everyone else.

Third, most of them don't take hitting very seriously.

They don't practice much hitting, besides bunting.
They are paid to pitch. And American League pitchers don't bat due to the designated hitter.

They are instructed not to hit players when pitching by the managers.

They concentrate almost all their efforts on working on their pitching.
Some exceptional pitchers were good hitters -- Don Newcombe of the Brooklyn Dodgers had a higher lifetime batting average than Roger Maris did -- not that Maris's was that great.