Your original post hints that your parents are willing to pay something, probably sufficient for UC or other public univ., but not for a private one.
As a parent who lives in CA, I can tell you this: unless your parents have been saving money for your college very early on, making $200K/year (before tax) doesn’t mean they can pay $60K/year (after tax) for your college education, especially if you are NOT the only child.
Also, as a parent, I can tell you this: the responsibility of parents is to try their best to provide you with an education, not to provide you with an education at a (costly) private school.
I don’t know if your parents compare you to other kids. But that’s a no-no. Likewise, comparing your parents to other parents is an absolute no-no.
Now, if you can prove to your parents that there’s something wrong with UC or CSU, they may be convinced to pay for your education at a private school. But I think it’s very difficult to prove there’s anything wrong with UC or CSU.
Did I tell you that I didn’t like entitlement attitude?