Responding a question with another question

This sounds like the argument of accepting the default position. For example, if someone asked me, "why don't you die your hair blue?" a reasonable response would be "why should I die my hair blue?" (a question). People are not obligated to answer questions. Asking for more information is justified in many cases. The default position is that people don't die their hair blue... people need a reason to die their hair blue, they don't need a reason not to.

Similarly, as an atheist, when people ask me why I don't believe in any gods, my answer could be "why should I believe in a god?" (or their particular god). However, I usually just say because I have not been convinced that any gods exist.

When it comes to your question about being vegan, the default position is not being vegan. People need reason(s) to be vegan, not reasons not to be vegan. So I think asking why is a legitimate response.

Sometimes, responding with a question is a way of trying to imply an answer thought to be obvious – just like asking the question in the first place is a way of suggesting an error in behavior.

For example, you ask me why I wear mismatched socks (implying my socks should match).  I respond with, “Why shouldn’t I?” (implying that there’s no real reason socks have to match).  I’m hoping your reaction to the question I gave as my response would be something like “Oh, I never really thought about why most people wear matching socks.  Now that you mention it, there’s really no reason socks have to match – keeping feet warm (or whatever other benefit one sees in socks) doesn’t depend on the socks matching.”  If that isn’t your response, it can get us into a discussion about the value of matched (or mismatched) socks … something that might have been the initial intended purpose of the discussion.

I suspect the initial question about why one wears mismatched socks is a proxy for the argument:

P1: I see your socks don’t match.

P2: mismatched socks is a bad thing because …

C: Therefore, you should start matching your socks.

I suspect my “Why shouldn’t I wear mismatched socks?” response is a proxy for the argument:

P1: wearing mismatched socks is a fashion choice.

P2: we are all free to make fashion choices.

C: therefore, there’s nothing wrong with me choosing to wear mismatched socks.

If we were to present the implied arguments as above, rather than as questions, we’d either agree or disagree.  If we still disagree, we’d probably switch the debate away from the two questions toward whether we can agree on P2 for each argument – taking us to what was probably the real meat (or vegetable) of the debate.

I’m not sure the questions represent fallacies as much as imprecise communication of positions and different understandings of the matter under discussion.