You should talk to a close family member and explain that it isn’t your fault you don’t know it, nobody taught you. You’re learning because you care and that shouldn’t warrant jokes. I bet speaking Korean and interacting with Korean culture will mean a hell of a lot more to you once you learn than it does to them.

My family (although not mean about it) is the opposite, when I say I’m learning Greek or that I’m interested in getting my citizenship they mostly just ask “why?” They say Christos Anestis come Easter and believe in the mati and think Tuesday is the unluckiest day of the week but learning Greek seems odd to them. The older family members speak it but saw no reason to teach me or my cousins.

It’s an odd thing to be definitively a part of a culture but not be able to speak the language that makes up that culture. Keep learning it, try to explain to them that it’s disheartening to get teased for trying to pick up their slack, and just keep swimming