Home prices could fall with mortgage rates.

Why?

Because monthly payments are the operative constraint for new home buyers.

Why?

Because the vast majority of first home buyers will pay considerably less than they do as renters, even if you don't deduct the capital accretion from their payment.

Why?

Because banks will lend freely to landlords but not to the working classes.

Why?

Because of an over correction since the global financial crisis. The principle that lending to owner occupiers is safer than it looks on paper, since people try hard to keep their homes is correct. But it can't be trusted since it was exploited to construct trillions of worthless paper.