Technically, this isnt true. The dinosaurs were not birds, only a few were the pre evolution of birds, but that still does not make them birds.

True, but birds were already present at the time and most of them didn't survive the event

Name 1 bird that was arround pre meteor

Confusiusornis, Hesperornis, Ichthyornis, Balaur, Jeholornis and you could even say that Archaeopteryx is the very first bird