The lack of empathy or compassion we feel for fish makes fishing seem like a pretty extreme thing to oppose on animal welfare grounds. “Oh God don’t tell me you love all the fishes in the ocean too now?!”
But we also have absolutely no reason to believe that fish don’t suffer and feel pain so why would we risk it? They have a central nervous system and they thrash about like crazy when hooked (as any proud fisherman will assure you whilst regaling you with takes of the heavyweights they’ve landed that day), they seem to know what stretches of water to avoid if continually returned to by fisherman (again, something keen fisherman will attest to).
So, until we are sure that they don’t endure a huge amount of pain and suffering when being hooked, played and reeled in, perhaps it would be best to avoid it altogether.