Why don't catchers wear batting gloves?

Answer 1

If they are holding on to their gloves they cannot dive palms down and road rash them, also outstretched fingers often get jammed on the base or cleated by the short stop. In the event they have to slide into the base, they stand the chance of ruining the gloves given they slide into the base using their hands. They slide head first and the gloves are expensive. I heard that some also do that to remind them not to slide head-first.

Answer 2

They do, when they bat.