I’m not saying you should take offence - I just know that it can be corrosive for people in that position. Being never seen as part of the culture does something to you, you feel apart, forever, even across generations.
I’m saying to give your fellow humans more consideration when you interact with them.
It might not affect you much because you didn’t build your whole life in Korea.
But imagine you are 3rd generation living there, your parents have been born in Korea but you still aren’t seen as part of the country. It builds resentment and segregates the citizens which makes life harder for everyone.
The reverse is also true: it can be corrosive for the people on the other side of that equation. Of course the 3rd generation "foreign" descendant had no choice on where to be born, but you can imagine that for the generation of the "natives" that took in the immigrants, it might have felt strange to see among their community people that looked different, spoke a different language, and had different cultural customs. It's hard not to think that this was corrosive to the social fabric, especially for the people who didn't feel that they had agreed to that particular change in the social contract.
> your parents have been born in Korea but you still aren’t seen as part of the country
Some immigrant groups don't integrate very well, even after generations. Naturally, it's a bit of a chicken-and-egg problem; do the immigrants not integrate because the natives reject them, or do the natives reject them because the immigrants don't integrate?
As an immigrant myself, I believe the onus is on the immigrant to integrate, and to raise one's children to be even further integrated. Again, it sucks for those who had no choice but to be born in a country as the descendants of immigrants, who nevertheless get judged as an immigrant unwilling to integrate; but that's not a problem particular to immigration. It always sucks to be judged not as an individual but as a member of a group.
We should all strive to judge people by who they are and not what group they belong to, which I suppose was your overall message; but I just want to point out that everything is a two-way street.