once I was even asked "Are you Asian or Chinese?"
I nearly slapped the guy.
For giggles I should note that in UK English Asian tends to refer to India, Pakistan, Bangladesh and such like. The China-Korea-Japan +Thailand thing would be oriental, something I am told causes some to take offence in the US. It can get a bit blurry at times but it is what it is.
In all honesty, unless the topic is brought up, I wouldn't ask.
Why would I care where you're from? (aside possible international trading)
Basically, you're just another human being in me eyes.
I'll treat you the same way as you treat me, regardless of skin colour/race or sexual orientation.
I mean, why would someones country of origin matter?
I am genuinely confused over the strong negative reaction you have here. First time I have seen such a thing, and I dare say similar things would apply to most of those that quoted you on it. I could possibly understand if you were mischaracterised it might get tiring for some, and a further failure of geography ("I'm from the UK" "oh I once went to Sweden" sort of thing) can also not help matters, but the mere question asked because the person is curious is never something I would have considered any kind of poor form to ask. Equally I can't see the mere question belay any desire or notion that someone intends to treat someone other than as a person.
There are questions and lines of conversation that have implications; I think I joked before that if someone asks me about my job then it is as big a clue as any that I am speaking to an American, and similarly if someone is telling me about their kids then I only really care if I know said kids in and of themselves. Again though a simple "where are you from?" is plenty innocuous as these things go, and actually a useful question.
To further answer the question of "why would someone's country of origin matter?" then if I am seeking common ground (fairly common in conversations with new people or people you are attempting to get to know better) then one's country of origin tends to provide a starting point for all the various forms of media and entertainment, geography, history, food, language, industry, politics/current events, sports, science and if I must be British about it then even the weather. It gets even better if your general hobbies are a bit obscure to begin with; I can't say I meet many ROM hackers or people interested in the maths and manufacturing of old school heavy engineering*, some like old machines but the approach there is quite often radically different, and if I start talking about anything that with a completely random person it tends to go nowhere and makes me look very strange.
*choice video