The consumer is de-leveraging and paying down debt, not taking on risky high priced debt, such as depreciating assets (houses).
The housing market is dependent on demand. Higher mortgage rates remove potential buyers (demand).
Diminishing demand means no pricing power = lower prices (basic economics).[/quote]
If those higher interest rates are accompanied by a recovering economy (including jobs) then there may be no net reduction in the number of buyer(demand). If the recovery stalls or reverses, rates are likely to dip again.