Well, since you're being frank, let me be the same. You're so busy clutching your pearls, that you're not grasping two main things:
1. When you're depicting a general/societal phenomenon (which white privilege is), there will be generalizations. It's the same when talking about black incarceration rates and education disparities. You can't talk about societal patterns without generalizations. So you either ignore it to avoid offending people or you address it and deal with the consequences. Although you said there are better ways to discuss this, you seem geared toward the former since you haven't accepted the fundamental reality that it's impossible to talk about white privilege without generalized language.
2. It's better to confront the negative aspects of yourself or of the population you belong to than to ignore them or have your hand held while talking them.
To explain, nobody likes to see themselves depicted negatively, as a group or as an individual. Regardless of wants, there are negative things about or around most individuals and groups. You can either confront them, whine when people point it out or request that people hold your hand in order to talk about it. Most people do the last two, unfortunately (which is what you're doing). For instance, there are black people who REFUSE to acknowledge problems within the black population that contribute to their socioeconomic place in society. There are white people who REFUSE to acknowledge problems within the white population that maintain inequality. And so on...
People just need to stop whining, acknowledge the negative aspects of their population or themselves and get on with it.