You are producing fragile hybrids that can't survive in the Level 1 Fish Environment that you have at the start of the game. Only common fish (the species of fish that you get from the common eggs) will stay completely healthy in a Level 1 Fish Environment. Most of the hybrids in Fish Tycoon require Level 2 or Level 3 Fish Environment, which you purchase in the supply shop.
There are other reasons for fish to die, as well. I have put links in
this post that will lead you to helpful information about why fish die, as well as some strategies to get started successfully in Fish Tycoon.
