Why don't birds cross breed?

Answer 1

They do sometimes. Generally in the wild there's enough of the same species around to allow for same species breeding. They recognize one another based on how their parents looked (they saw their parents, they like birds that look similar), and mating rituals different bird species have.

On the other hand if you have 2 birds of similar but different species, in captivity where there is only a few options to satisfy their mating urges, they will bond and mate with different species, that's how we get hybrid species. (Sunday conures, Harlequin Macaws, Catalina Macaws, and many others). Birds can't interbreed to just any other bird though like dogs can.

Answer 2

Actually some do and result in hybrids. Take the golden-winged warbler and the blue-winged warbler for example, they're completely different species and yet they manage to mate and have a chick. This peculiar chick is known as a brewster's warbler. But many other hybrids exist, but mostly only with warblers and sparrows. However, there are consequences. The hybrid cannot mate and have chicks of its own. This is the case with all hybrids.