Greenhouse gas emissions shouldn't be the only factor people consider for sustainability of their food. In the case of fish, this very article talks about the issues with farmed fish. Even a plant-based diet can be filled with unsustainable sources, such as plantations that destroy endangered habitats for palm oil, or industrial farming operations that spray lots of pesticides to harm the insect population and allow lots of fertilizer runoff into natural waterways. We're still polluting and depleting resources for many many vegetarian foods in the world.

I'd argue that if we're looking for a full top-to-bottom sustainable food system, animals will play a role. But we need to be cognizant of the whole system, not playing whack-a-mole with issues.