Depends on the fish. Some fish are real tough and can handle it, some are not and they are pretty much gonna die after you hook em and handle them. Bass for example are tough as nails and they are pretty much thought of as a sport fish. Usually they are in dandy shape after the catch and you can weigh them and release them. Let the next guy have the fun you had. They improve with age. (Tougher, Smarter, Faster)
What is the fun of catching something you don't intend to eat?
It's a sport. The thrill of the catch, the ensuing fight, the satisfaction of the catch or the crush of defeat when he spits the hook and laughs at you while he swims away. It's exhilarating. If you happen to catch invasive species in the process you can cull them and help preserve the ecosystem for native fish.
I kind of get it, but it fucks up my theological thoughts.
You are using your superior human intellect to trick, and catch, and potentially release, some dummy living down in the muddy waters.
And then, with your perfect human benevolence, you catch the dummy, drag him into the air, talk to him (I have seen that most fishermen actually say something to the fish, i.e. 'You are huge!', 'What a fish you are!', 'You dirty, back into that gross river with you'), and dump that fish back from our Aether, back into his muddy water.
It just reminds me a lot of the behavior of the Old Testament God, and how he would talk to his catch-and-release prophets.