I was reading about a dam demolition in Washington a while back and the bit that really helped me wrap my head around it was this:

Salmon are one of the primary pipelines to transfer calories from the ocean inland.

Those calories—by that I mean a shorthand for "nutrition"—naturally get washed from land out to sea by stuff dying in rivers, rainfall, etc. Without some engine that cycles that material back into inland areas, you don't have a functioning cyclic sustainable ecosystem.

Salmon get eaten by bears whose poop feeds plants that are eaten by herbivores. An incredible amount of the natural world in salmon areas depends on this pipeline running. When you stop the salmon, you stop the entire circulatory system.