"Is it possible to just be to uncoordinated to dance? I don't mean physically disabled, just too uncoordinated."
It is certainly possible to have not learned coordination yet.
Consider a young baby - he or she cannot walk. Some of that might be a strenght issue, but most of it is that the mental pathways to coordinate movement and sense balance have not yet been developed. The infant brain is quite ready to form them though, so it doesn't take long.
Consider an older adult trying to learn to walk again after a stroke. The original pathways for coordination are gone, and new ones have to be learned. At first they will be uncoordinated, and the adult brain is not quite as ready to build new ones as the infant brain, but it can be done.
Compared to learning to walk after a stroke, learning to dance isn't too bad. However, physical therapist are a lot more helpfully specific about what to do in order to learn coordination than your average dance teacher is. If you had a dance teacher who was a PT used to working with stroke victims, I bet you'd learn really fast!