But the world now is a world with humans, and anything that isn't adept at surviving in this environment will become extinct.
Why should we try and save them?
IMHO doing this is interfering with nature rather than letting natural selection take its course.
It's not interfering with nature because nature is not killing them we are! If humans collectively didn't over-populate and destroy everything they touch they probably wouldn't be facing extinction. And I have to say with an attitude like yours haircut you would have gone far in 1930/40s Nazi Germany.
You obviously don't like it, but I am looking at this from a purely scientific viewpoint. If those last Maui dolphins disappear what difference would it make?
Can someone explain to me exactly why it matters if a species becomes extinct?
Millions of species have become extinct since the dawn of the Earth. Those that don't adapt to their environment die out, those that do thrive.
Sure the environment may be changing due to people, but if some species die out because of it why is this necessarily a bad thing?
There will still be species that thrive and these will be the successful species for the future.
Nature will find a way to keep things in balance and short of not being able to see something in a zoo or feeling bad becuase it has died out what difference does it make to the grand scheme of things?