It's sometimes someone who has never really thought about animals rights and wants to learn more. But more often than not, the questions come from someone who wants to trip you up and "prove" that animal rights is a lot of hooey.
"If you were in a lifeboat with a child and a dog and you could save only one of them, which one would you save?"
"If lions can eat meat, why can't people?"
Although on some level, it doesn't matter what your answer is. You could have the most logical, compelling answer to these questions, but if the other person is not ready to seriously consider animal rights, they won't hear you.