Why do rabbits and bats have large ears?

Because us humans have bred them that way. Someone got a rabbit with floppy ears, thought it was cute, and decided to breed from it.

In the wild, floppy ears is no good. Reduces hearing sensitivity and increases the risk for ear infections, for both rabbits as well as floppy eared dogs. But as pets, it doesn't matter. They survive well enough anyhow.