They're mammals, because we've decided that anything laying eggs are birds or reptiles (I am voluntarily skipping other arbitrary criteria), and anything giving live births are mammals (again, I'm simplifying here). That's okay then to put bats in the mammals category.
But this way of classifying is rather recent. If you classified animals in groups using other arbitrary criteria (for instance: if it has 2 legs and flies, it's a bird), then you would put bats with that group.
You cannot say their classification system got it wrong when you are judging it against your own, different, classification system.
Let me take another example. Certain cultures associate colours with emotions or situations. Assuming you're Western European or North American, you likely associate mourning with black, while if you were Chinese, it'd be white, or Eastern European it would be yellow, or South American it would be purple (ref: http://www.informationisbeautiful.net/visualizations/colours-in-cultures/).
Are all the other wrong because they're not using the same classification as you?
So it's true, everyone now agrees on the same classification system for animalia based on certain (arbitrary) characteristics. Don't forget it's a recent phenomenon and documents produced prior to using this classification system is not bound by it.
