Question for the baseball guys

[Mark Padgett]

I saw a thread on the baseball forum about a batter changing batting boxes during an at-bat and, as I thought, it's not illegal (as long as the pitcher is not ready to pitch), but one of the posters mentioned that a pitcher cannot change his pitching arm during an at-bat (NF rules). If this is correct, can you explain the reasoning behind it? If a batter can switch, why not the pitcher. That doesn't seem equitable to me. Thanks.

And no - before someone thinks of it, by the term "change his pitching arm" I don't mean he can replace one with a new one if it wears out.