Property taxes are fundamentally regressive because if two individuals in the same tax jurisdiction live in properties with the same values, they pay the same amount of property tax, regardless of their incomes. That's the literal distinction between progressive and regressive taxation. The fact that the middle class household can offset the burden by getting a smaller place is quite irrelevant.

In addition, it's erroneous to think that property taxes are shouldered by landlords. They are, in fact, passed on to renters.