I suspect it’s partly just coincidence. Prior to the K–Pg extinction, the sky was ruled by non-birds. Pterosaurs. In fact, the late Cretaceous saw some of the largest creatures to ever fly, like Quetzalcoatlus and Hatzegopteryx.

At the same time, it was also not mammals that ruled the ground, it was, as many an eight year-old can attest, dinosaurs.

The K–Pg extinction event may have killed off all the non-avian dinosaurs and pterosaurs, in part because of their larger size. So the very thing that made them “rule” before is what killed them off, and conversely, the very thing that kept avian dinosaurs (i.e., birds) and mammals from ruling during the Cretaceous is what allowed them to survive that event and evolve to fill the many niches vacated by non-avian dinosaurs after the event.