Do you really know what white privilege is? You can’t boil it down to one particular scenario. It is a systemic imbalance in countless aspects of one's lived experience. If you give me one scenario, I’ll give you a counter scenario, like being black on a college application. That rhetoric doesn’t work and only pisses people off.
There is white privilege, but don’t talk about it with the white men you describe. Talk to them about class privilege. For them, class privilege hurts them more than white privilege helps them.