This is technically correct, but I think this misses the point. Unhabitable future Earth with molten icebergs and polluted gray sky may, technically, be a "natural change" and a consequence of "natural" human actions.
But we, humans, want to avoid this future. The same goes for causing extinction of most wild animal species.
Edit: to expand on GP's point: imagine your house burned down, and somebody said "> Your property wasn't destroyed nor hurt in anyway. It just changed". Yeah, all the atoms are still there, but it changed in a way we find undesirable.