It’s no myth that cats are natural predators, and, yes, they do eat birds. But nature lovers have unfairly exaggerated the role that cats play in decimating bird populations. While cats do indeed eat birds, they also eat mice and rats, which themselves are notorious for preying on young birds and eggs.
Cats actually aid birds by keeping down the population of egg predators. (Cats do not eat eggs.) Cats also prey on several other egg eaters—blue jays (the most notorious nest robbers in the world), young raccoons, young opossums, and the like.