You're right that at carrying capacity, the limiting factor is food and space.
But most of our fisheries are far below that now. Fish can only breed as fast as there are breeding fish available, but we're eating them faster than they are being born.
You can view a fishery basically as a giant fish-making factory. If you eat away half your fishery's biomass, then to a very rough first approximation, your factory will only produce half as many fish.
One reason is that many governments are essentially paying people to take fish out of the ocean [1], to the tune of tens of billions a year. Japan, China, and Taiwan are some of the main players. They do it to keep fishermen employed.
Related to this: because technological change has made it really cheap and easy to catch fish [2], and up to now, that has more than offset the decreased productivity from damaging our fisheries.
But most of our fisheries are far below that now. Fish can only breed as fast as there are breeding fish available, but we're eating them faster than they are being born.
You can view a fishery basically as a giant fish-making factory. If you eat away half your fishery's biomass, then to a very rough first approximation, your factory will only produce half as many fish.