(non-religious answer)
Humans are currently the most intelligent and versitile species on the planet, otherwise they are really nothing special, flesh and bone, organic matter just like other creatures on the planet. Yet they manage to impact their environment and use up more resources than any other species. Humans have the intelligence to see the impact they are having on their environment and make predictions about the future, and they have the power to reverse at least some of the changes, but that would mean every single human, rich or poor, making major sacrifices for the greater good, and I really don't see that happening. The population growth as it stands today is just not sustainable, and something has got to give; unfortunately at the moment, that's other species whose habitats are being destroyed because more land is needed to feed the humans. Mass extinctions have happened in the past, and will surely happen again - it's just a matter of time. So I see the anthropocene era as being an interesting period of the Earth's history, but not a permanent one.
Ultimately, in a few billion years or so the sun will swell up into a big, angry red ball and swallow up the Earth and that will be the end of all traces of humanity. Except maybe for a few space probes travelling alone in the depths of space.