Birds are not mammals. Fish are not mammals. Mammals on the other hand have males that impregnate the females.
Biology is messy, the boundaries are messy, the words we use are merely for our own benefit to simplify a messy and complex reality.
Your abstraction ignores all the sterile men and women too, by the way. That's because it is a particularly bad one.
You're the one who wrote:
> Mammals on the other hand have males that impregnate the females.
We're all saying "that's not a very useful definition".