There's not a huge amount of logic to it (and I say that as someone who held that position, before I turned vegetarian).
Actually, the only logic is that if most people come into contact with rabbits, it's as pets - a friend's, a school, a garden centre. It's like eating Fido, and there are plenty of posts on here, discussing shtf, where lots of people are saying no, I'd never eat Fido (and a few saying they would, of course).