Plesiomorphy and symplesiomorphy
Apomorphic and synapomorphic characteristics convey much information about evolutionary clades and can be used to define taxa. However, plesiomorphic and symplesiomorphic characteristics cannot.
A backbone is a plesiomorphic trait shared by birds and mammals, and does not help in placing an animal in one or the other of these two clades. Birds and mammals share this trait because both clades are descended from the same far distant ancestor. Other clades, e.g. snakes, lizards, turtles, fish, frogs, all have backbones and none are either birds nor mammals.
Note that some mammal species have lost their hair, so the absence of hair does not exclude a species from being a mammal. Another mammalian synapomorphy is milk. All mammals produce milk and no other clade contains animals which produce milk. Feathers, and milk are also apomorphies.