I put "destroy" in quotes since I think that's ridiculously loaded. The biosphere itself is naturally unsustainable at its current complexity for more than 1 billion years from now[0], the Sun is going to go red giant past the next 5 billion years, and, as far as we know, the universe will end in heat death. Entropy and transformation is inevitable. Humans contribute to that, but doing it in the service of higher cognitive functions by which the universe can know itself should be the noblest reason for it to happen (from a human perspective), no?
Another counterpoint: what if humanity only becomes worthy of spreading itself in civilizations that can only form post-Earth (too far into the future to still be living on Earth)? Should those be condemned to non-existence because humanity's original nucleus didn't bootstrap itself impressively enough to earn a chance at outliving its planet?
0: See https://en.wikipedia.org/wiki/Timeline_of_the_far_future and Ctrl+f "c4 photosynthesis"