If you're referring to white privilege fueled by white supremacist policies -- and White people being honest about how they benefit from those unearned advantages (at the expense of Black and Brown people), then I agree with you.

But, as a result of those policies, hypocrisy and double standards being upheld. That isn't equality. So, fixing those injustices shouldn't "feel like oppression" to ANYBODY.

BTW, "whiteness" is an extremely nebulous term, and people who use it need to be very clear about how they're defining it. In a majority of cases, I assume they're using it synonymously with the terms "white privilege" and "white supremacy."