Why are bats mammals instead of reptiles?

Bats have fur, are endothermic, feed their young with milk, have a neocortex in the brain, have three middle ear bones, and have one fenestra (hole) in the skull below the postorbital and squamosal bones. These are all characteristics of mammals. Except for endothermy, they are all unique to mammals. Reptiles fit none of these descriptions.