So this is a bit of an explain-y thing, but there are reasons(pinging any shabbos-observant people for later in case I miss something). This is how I learned it.
1. The rule starts out in the Torah as specifically a kid in it's mother's milk. Later rabbis deduce from that rule that there is a more general rule(based in repetition) on mixing milk and meat from land animals with milk. Or the rule was preserved orally and then written down.
2. At this point, fowl and milk is still OK. This starts going towards being not done because people tended to treat fowl as meat. There was a period where this was a varying custom, with some regions observing it and some not.
3. Eventually, due to issues with confusing fowls and other meats, issues with "meats you can mix" and general worries about perpeptual rules-lawyering about what is and isn't a permissible meat to mix, eventually later Talmudic-period rabbis just say "stuff it, no meats and milk period". At no point does fish enter in, presumably since it's harder to mix with say, chicken. Also, fish doesn't usually get treated as a "meat" the same way as say steak or chicken is.