I read the Torah, and that’s what it says there. The whole derivation is about a kid in its mother’s milk. Let me ask it more concretely: why not fish meat too?

A. — good thing you didn’t conclude that “everything written in the Torah means specifically in its own mother, but some other mother is no problem for us…”

As for the slip in the Beit Yosef: fish and milk is a fairly pathological example of ossification creating Jewish law out of nothing. The Beit Yosef writes that it is forbidden to eat fish with milk (because of danger). The Rema suggests that it should read fish with meat (“and therefore it seems that meat with milk got mixed into the Rabbi’s text,” although that is a forced gloss that doesn’t really fit the context), and in any case he disagrees in practice. And after him came a whole line of major halakhic decisors (cited in Yechaveh Da’at, among them: Perishah, Shakh, Pri Chadash, Taz, Magen Avraham, Chida). None of that helped, and afterward later authorities of the Mishnah period came along and, on the basis of various rather flimsy sources, stabilized this ruling. The problem is that these stabilizations would never have been enough at all if it weren’t written in the Beit Yosef (at least as far as I know, and my knowledge is limited). The whole topic of meat and milk is one of the biggest halakhic mountains hanging by a hair of the holy beard, and after the theological diet perhaps the time will come for the halakhic haircut too.

On the prohibition of fish with milk, see Rabbenu Bachya [cited in the introduction to his book]: it was known to physicians that there is danger in eating fish and cheese. That is a crushing blow to those who speak against the Beit Yosef, or to those who claim that cheese is permitted [you have only what the Sages prohibited, even when it is not understood].

To Nur
1. Since when are halakhot meant for medicine?
2. Why, in practice, is it permitted after the fact to eat fish with milk (see Yalkut Yosef part 2, the law of eating fish with milk or meat): “It is enough for us to be stringent initially not to eat fish and milk, but after the fact, if they were already cooked together with milk, they are permitted to be eaten.”
But fish with meat is forbidden even after the fact.
So how can it be that if it isn’t healthy, suddenly after the fact it becomes healthy?

By the way, apparently fish with milk was something accepted in the time of the Talmud — “fish that was placed in kutach.” Now, the Sages prohibited poultry with milk as a fence, because it might look similar to meat with milk. Today we ask, so why is fish permitted? Because apparently today, and especially in certain parts of the Jewish people, people don’t eat fish with milk, so it seems natural to us to compare fish meat to beef.
But back then there was no such comparison, and people thought only that poultry resembled meat.
It is possible that if Jewish law were being established מחדש today, they would also be stringent about fish and milk and require waiting.

It seems to me fairly clear that Rabbi Ovadia also understands that this prohibition is baseless and that there is no danger at all. But in order not to make changes and not to show disrespect to the halakhic decisors who brought it, he says that ideally one should act that way.