I have never been too sure of my stance on this issue, partially because I am not committed to the idea that human extinction is in the planet's best interest.
First of all I would like to note that the most egregious offender of environmental destruction is well, the environment itself. I think we need to be honest about why most people who care about the environment do so: to maintain human existence.
The other option is that of utilitarianism. In that case we give all organisms equal consideration of interests. We strive for the least amount of suffering across the board and the most amount of autonomy. I find myself somewhere in this vein.
The problem is that by these ethics, theoretically, it would be unethical for humans to purposefully end themselves in order to keep other organisms from suffering. The reason is that humans have the capability to actually reduce organism-wide suffering due to natural causes. This can be through technology, and also through "green" stuff like certain forms of permaculture. Now we certainly are not on the right track now, but I do not believe that has anything to do with "human nature." I mean shit, I left the church for a reason.
Either way, it doesn't seem particularly important to me as mass extinction events is inevitable. At least for the time being. It is surprising how few people are actually aware of some of the perfectly natural processes at work. Take Yellowstone for example. That place is a fucking ticking time bomb. It is a supervolcano that seems to erupt every 40,000 years (the last eruption was...40,000 years ago). When it erupts, the entire midwest, most of the west coast, and parts of the east coast will be destroyed. Several states will disappear by the blast alone. The ash depositories will most likely result in a rapid volcano winter worldwide- this could lead to another ice age. A supervolcano came dangerously close to annihilating humans once before. Our data indicates that the population possibly dropped as low >1000 worldwide. Granted we had not spread out though.
Anyway, the idea that there is something inherent about nature that deserves our respect is laughable. Nature doesn't give a shit about nature so we should we by those principles? If we are to actually care about anything other than our own species, we must arrive at our conclusions through a blend of logic, intuition, and practicality.