What's wrong with the generalization?
It's not accurate. When I think of "left-leaning" social programs, I think of welfare, Medicaid, etc. Programs that support home ownership, perhaps too aggressively, are supported at least as much, if not more, by right-wingers.
I agree the issues with the proper incentives for home ownership are complicated, and probably swung too far to supporting it in the last 20 years.