Is answering a question with a question rude?

not, rude but annoying, why? do you find it rude? (sorry but i just had to do that!)

No. The reason why people do this is because they are often not sure why the person asked the original question. So they question the question. It isn't rude though, it just expresses concern.

No it's not rude.Some people find it rude because they think the other person is prying but it's more about people not wanting to talk about feelings.

Umm no I dont think that should be rude, it does depend on who you say it to and in what context.

Yes, usually

But people in America are generally douche bags

Not to me. Some people see it as trolling.

no ancient monks used to do that... what sensai said 私は何を言っていますか

It depends what you reply with, and how you say it. So yes and no.