In a way, the carnivorous/herbivorous discussion is meaningless with today's technology and nutrition understanding. We can make totally vegan diet for what are called fully "carnivorous fish" like white seabass that actually out perform fishmeal based diets.
What we call carnivorous fish need taurine (like cats do), but that is just a cheap synthetic amnio acid that is used in your energy drinks. Carnivorous fish also aren't very good at handling some of the carbohydrates found in vegetarian diets and we have been breeding soy beans to have fewer "anti-nutritional factors". So called herbivorous fish often have problem with high lipids in their diets, but are better at metabolizing carbohydrates.
The big distinction in public perception was created by environmental activist as part of a succesful de-marketing attack on aquaculture in the US. I really don't understand how and why the eNGO ended up supporting bottom trawling and wild fisheries and opposing aquaculture, but it sure isn't based upon science. Aquaculture growth is zero or negative in the US and double digits everywhere else in the world (including Canada and Mexico).
They make big claims about fish-in fish-out ratios and other nonsense and the use of fish meal in fish diets, but fish meal production world wide has been a constant for 4 decades while aquaculture has grown world wide from a trivial amount to equal the ocean fisheries in that same time period at double digit rates. The fish meal market just shifted from pigs and chicken feed to fish feed. It is hard to visualize a market shift as being environmentally significant.
As the fish meal prices increases the soy bean organizations took advantage of the market openings. That is just economics adapting to the shifts.