I think your mum identified a real cultural difference, but she's blaming it incorrectly.
Your point #2 is spot on: as you grow older you're expected to do more things your own way, than you did as a child. Take some risks, learn with mistakes, get other things right. That's so biological that even chimps are like this too.
So at least some level of "let me cook!" is expected. Even if your family stayed in China, or if moved elsewhere than USA.
However, that does interact with culture. Because we humans want two things:
- independence - the ability to act on our own
- community - support from our own peers (family, friends, etc.)
Both are desirable, but mutually exclusive - you can't have your cake and eat it too. But how much of each we give up for the sake of the other depends on culture. And based on a lot of things I think people in USA are expected to focus on #1 at expense of #2, while people in China focus on #2 at the expense of #1. (That's a continuum, though. Nobody is giving up all their independence, or all their community.)
And that's bound to interact with how adolescents are expected to behave. With your parents being raised to expect a lot less independence of you than you, being raised in USA, want.
So… do you think Americans (or Westerners in general) are “too rebellious”? Were you “too rebellious” growing up? If you have children, do you think they are “too rebellious”? Should kids be being “more obedient”?
My family wasn't even remotely healthy so it's poor grounds for comparison. But let's say I learned rather quickly how to do my own thing while pretending to play along a screeching mother, who dumped her stress on her two children. (For reference I'm from Latin America, and almost 40.)
I don't have children. The nearest of a "filial figure" I have is a nephew. If anything I think he's a bit too obedient.