OK, I understand what you're experiencing now! In the beginning of the game, your tank environment will not support hybrid fish. Depending on which fish you breed, they will lose health at various rates. As you've seen, some hybrids will die as babies, others will live longer but continue to lose health until they die (or you sell them).

There is no cure for that kind of declining health apart from researching better fish environments. Since you're at the beginning of the game, you won't have enough money for that for awhile.

I posted one approach for getting started successfully in Fish Tycoon
here.

You might give that a try until you get more familiar with the game and can try strategies of your own!