Species are transient, and we'd have to really destroy the planet so that it is inhabitable for any species. We might make it hard for humans to survive, and take a good percentage of collateral damage species with us, but Earth will be sustainable for some species for billions of years.

There's two different discussions here, one, will mankind see Earth to a point it becomes destroyed, and two, will the Earth eventually be destroyed naturally? Even if we wiped out all war, diseases/cancer/sickness, ended world hunger and poverty, we're kidding ourselves if we think mankind as a species will be around when the Earth is destroyed billions of years from now.

The Homo species have been around for about 1.5 million years, and homo sapiens have existed for approximately 300,000 years. We only started forming civilizations 6000 years ago.

That's not even a fart in the wind in terms of life on Earth.

The 'age of the dinosaurs' lasted 165 million years, and ended 65 million years ago.

Earth will be destroyed at some point billions of years from now when the Sun dies. There will probably be life forms up until the time the Sun no longer can sustain any life, and that will be a long time before it's actually destroyed.

To think mankind can survive for the long haul given our history of self-destructive tendencies is laughable at best, but life will sustain on Earth in some form or another long after we are gone.