There are two sides to it. The other side is: what people consider current "balance of nature" is just a transient state. Species die off all the time, ecosystems last millenia and then suddenly collapse, then rebound and look completely different. Protecting the habitability of our planet is paramount, but overindexing on how any particular aspect of it looks at any moment is a fool's game.
Scale matters and modern humans drive species to extinction faster than the historical average by several orders of magnitude. Even if you value non-human intelligent life at zero, which I think is morally reprehensible but know plenty of others disagree, this kind of destruction has significant hard to predict impacts.
> Species die off all the time,
This species didn't just die, it was exterminated by humans. It is the difference between someone dying fro a sickness and from a bulled to the head.
> overindexing
How can be stop fishing species to extinction "too much"? How can you justify that way of thinking in this concrete case?
This is true of trees even. People think forests have looked the same for all time but trees are frequently pushing each other out of areas. Disease and pests play a huge role as well.
There's some amount of introduced pressure due to invasive species of both trees and pests but it's always been this way. Everything is in flux all the time.
Stable pockets exist but they're relatively rare.
The planet will literally survive anything. Life finds a way. There were supervolcanoes that blanketed the skies for millions of years.
But human civilization as we know it is fragile.
But from a purely selfish and human centered perspective we can also demand preservation just so that future humans also get to enjoy what the previous generations had. I wish humans didn't kill off the dodos! I want my grandchildren to be able to eat ocean fish. And I'm willing to reduce my own fish consumption if that means the fisheries live on into my grandchildren's times.