To many environmentalists, sustainability means leaving the world the way you found it. I think that this may reflect the instincts of a hunter-gatherer.
If you are a hunter-gatherer, how much you can eat is limited by the natural rate of replenishment. If you eat game or plants faster than they are replenished, your tribe will die.
Modern human welfare is not governed by replenishment. We use knowledge to add value to our environment. Cultivation of crops means that we can grow more food than we could obtain by gathering. And we apply ever-increasing ingenuity to this cultivation.
Sustainability of modern life is thus much more complex than sustainability of hunter-gathering. Our modern ancestors have left us the gifts of their ingenuity, so that what they took out of nature has not hurt our welfare. And we are likely to do the same for our descendants.