Others are making the good general case argument, but I will add one other thing: sometimes there's actually some very positive "side benefits" that you get from having a biodiverse ecosystem around, that you may not initially think about as far as the general conservation case is concerned.

Examples that come to mind immediately include the huge number of medicines that have been derived by isolating compounds derived from plants, an area which we are probably far from done exploring. Another more specific case I can think of, is how one of the most important compounds in molecular biology today (Taq polymerase) came from bacteria found in the Lower Geyser Basin at Yellowstone. (https://en.wikipedia.org/wiki/Thermus_aquaticus)