His father went to U. Wash. under the GI bill. I think the point @MikeTheBard is trying to make is that Gates the Current is an example of generational upward mobility, which is consistent with the American dream myth, and not really comparable to dynastic wealth (which to many of us feels amoral).
What’s problematic with the Gates story is not that he was able to leverage his background the way he did, but that it is so much harder for people today to follow a similar multigenerational trajectory.