You make a solid point. Privilege, from an objective viewpoint, in a country of laws, only deals with how the law is applied to the individual. The rest is just subjective excuse making for why people have stuff you don’t have.
And yes, regarding “Privelege”, from a legal standpoint, there is no white privilege, but there most definitely is (or at least was) black privilege with things like Affirmative action.
Sh-h-h. Don’t let them find out about our secret handshake. Or all of the freebies whites get like interest free mortagages and free utilities or the fact the the internal revenue secretly refunds all white peoples tax payments. Or the fact that our bosses let us laze around and make sure only blacks work. Boy, if they find out about all the secret bennies of white privilege they’ll really complain.