The practical one is that humans rely on ecosystems being the way they are, and that unbalancing them disturbs our interests, particularly in agriculture. We also rely on a diverse plant ecosystem to discover and develop new medicines.
The second argument is more values-based: that ecosystems and animals have value in and of themselves, axiomatically. If you don't appreciate this argument perhaps you never will: it's not something that draws on more fundamental principles, it just is a principle itself. Similar are arguments about speciesism and the active right of sentient animals to survival: it's probably one of those things that can't be deconstructed into more basic, falsifiable arguments. I'd suggest the same applies to the claim that human progress is necessary and valuable - it doesn't seem provable, just an instinctual belief.
There might be a third argument: that protecting the environment helps economies optimise for longer term gains. One of the things holding back sustainability has been the relative cheapness of dirty alternatives - so restricting mining might encourage more creative means of manufacturing. And frankly, if all you're doing is mining cadmium for smartphone batteries, you may not be doing the human race much good to begin with.