A single family home is presumably owned by a single family that is actually living in that home. A large building with many apartments is owned by a wealthy landlord who is less likely to be living there. Of course the wealthy landlord should be taxed much more than the single family, that’s just common sense.

The problem is that the single family that can afford a whole house in a city, while less wealthy than the big landlord, is likely more wealthy than the tenants in the apartment building. Because the landlord is able to pass down the burden of the property tax to the tenants, the property tax becomes regressive.

There is no way to solve this problem by simply changing the rates around. If you lower the property tax on large buildings, it is not guaranteed to ease the burden on tenants. You will likely just end up increasing the profits for the landlords. A true solution requires a systemic change that taxes the landlord, but prevents that tax burden from being passed down to the tenants.