I don't think that attitude is unique to Chinese people. My experience is based on my name rather than looks. Whenever people from my father's country ask me my name, they suddenly expect me to speak their language - and then to tell me what a shame it is when I don't. I've seen the same for British Germans, Polish and Vietnamese too!

One of my computer science professors who defected from Cold War Hungary was very anxious to meet me. It turns out that my Korean Catholic name is also a perfectly cromulent Hungarian name!

Well, that makes sense. If they thought you were a Chinese person, I could see why they would have asked you if you could read Chinese.

By that point in the conversation, however, I had already conveyed that my parents were from Korea, and I was born and had grown up here.

As someone who is learning Chinese (and VERY bad at it), (almost) every Chinese person I've met has been super encouraging and helpful. Most of them are surprised I'm learning it at all. But they also express encouragement differently, so I'm wondering if it is a misunderstanding.

That could well be. Some aspects of culture are quite subtle. There was this thing where, whenever some driver in traffic made me brake hard, my Chinese born wife would shout, "BE CAREFUL!" Well, here's the thing: I am very careful. I couldn't be blamed for any of those incidents. It's precisely that I'm careful that I was able to avoid a collision. It seemed very unfair that I should be blamed for any of these incidents. (Example, the car ahead of me spots a parking space at the last minute, then slams on his brakes to get the parking spot.)

So after about the 5th time like that, we had the argument. It turns out that she was just being scared and telling me to be careful, not knowing how an English speaker would take that contextually.