Holy unrealized irony.
No, saying that you are privileged does not imply that you are better than people. Saying that you're entitled to that privilege, or that it does not exist and what comes with it is deserved and natural: that bears the presumption that you're better than other people. Do I think that you consider yourself better than nonwhite people on the basis of your skin? No, that would be a pretty steep presumption. I just think that you're intellectually lazy and that you perceive the term/concept to be a slight against you, so you recoil reflexively.
And, yes, minorities use the term and acknowledge the reality that it describes. Meanwhile, obfuscating and ignorance-languishing threads like this are pretty much only made by the dumbest of white folks (or the very dumbest of nonwhite folks) to bitch about how the well-educated university types just aren't woke to the natural meaning of racial hierarchy like you brainiacs.
FWIW, I would prefer different phrasing at this point, since the color itself is downstream from the concept (it could just as easily be black privilege in a world that civilized differently) and the term "white privilege" just ends of distracting from the actual topic with dumbass conversations like this one. But I don't have the power to change that.