What does it mean when a person answer your question with another question?

It's often a "fogging" technique to confound the questioner and buy time before responding to the original question. A classic self-assertiveness strategy; useful if used sparingly when being, for example, unduly pressured to answer a possibly intrusive or bullying question.

Or, it could be that the person genuinely wants more information, some clarification of key points, or whatever, in order to be able to provide a fuller, more carefully considered answer.

So, maybe the person is being awkward because s/ he wishes to avoid the question; or s/ he simply wants to give as good an answer as possible. Determining which is largely a matter of considering the question's context & the relationship between questioner and respondee.