There’s a historical reason for this. The main restriction on eating meat (beyond what animal you can eat and various other “prep” rules) is that you can’t eat milk and meat. Specifically, you can’t boil a kid in it’s mother’s milk. This was seen by ancient Jews as an abomination and morally bad.
However, you can’t always tell what animal the milk and meat came from. If I have a steak and a jug of milk, do I know that the steak doesn’t come from the child of one of the cows whose milk is in the jug? I don’t know. Chances are it isn’t, but better safe than sorry so all meat can’t be mixed with milk. (Thus, no cheeseburgers.)
But what about chicken? Obviously, chickens don’t produce milk so it’s impossible to cook chicken in it’s mother’s milk. Technically speaking, chicken parmesan should be fine. Except, at some point in history, rabbis got worried that people would eat beef thinking it was chicken and would accidentally mix milk and meat. (I guess people were real idiots back then because I’ve never mistaken beef and chicken.) Therefore, all bird meat was restricted and forbidden from mixing with dairy products.
Meanwhile, fish was never, apparently, mistaken for beef and do remained restriction free when it came to dairy. I can toss a big slice of cheese atop my fish sandwich with no “milk and meat” kosher concerns. (Well, unless we get into rennet, but that’s a different topic.)
Unfortunately, with Judaism, there isn’t a central authority that can say “X rule is outdated and doesn’t need to be followed anymore.” It’s a very decentralized religion and this means that there’s a lot of momentum to the rules. Some changes can take effect in some Jewish communities, but getting widespread change across the entire religion is difficult.
