Generalisations made about minorities are usually considered bigoted because they're untrue, insulting and harmful, not simply because they're generalisations. If I say that veterinarians tend to like animals, that's a generalisation but not bigoted in any way. If I generalised a negative trait, like athletes tend to smell like sweat when they're working out, it's still not bigoted.

When people say "white people have white privilege", it's mostly a claim about a societal norm and not always specifically about an individual person. But even if we want to analyse it on an individual level, we still have a claim that's difficult to argue against. For example, saying white people have white privilege is to say that white people usually don't get pulled over for "driving while black". It's a generalisation, sure, but it's hard to imagine a situation where a white person has regularly been pulled over because he looks black. Similarly, I don't see it being a common occurrence for white people to be systematically filtered out of job prospects on the basis of having black-sounding names, because generally they don't have black-sounding names.

When you remember that "privilege" is a very large set of these attributes, even if you think of outlandish and rare cases where a white person might fall victim to them (maybe in the dark a white guy looked black in his car and a cop pulled him over, or maybe the guy was named after his mother's favourite literary character which sounds like a stereotypically black name and it affects his job prospects), the fact is that these freak chance events are exceptions to the general rule of their life. And that's why it's essentially impossible for a white person to not have white privilege (especially in societies where this discussion tends to take place and often even in other societies).