Cats are not like dogs in the way that their behavior has not significantly changed from their big-cat ancestors (they’ve mainly just gotten smaller, cuter, and more willing to tolerate people). As others have said, they still have a strong instinct to hunt, and birds are just part of their natural prey. They probably taste pretty good.
Also, as @Amurph said, cats are attracted to movement. Cat eyesight is pretty limited compared to ours; in exchange for their “night vision” they have sacrificed full-color vision (most cats are red-green colorblind) and the ability to detect fine detail. Thus, movement is one of the main methods of detecting prey. Obviously, birds move a lot and in interesting ways, which sparks the instinct to hunt.
It is probably also a fun challenge to catch a bird. All cats like to have fun!