I don't think it's necessarily the population that's causing the problems. I think it has more to do with how much damage a single person can do to the environment. Imagine how much impact you have on the environment compared to wild animals that are simply taking what they need, contributing to the natural order of life and eventually coming to an end and further feeding the process. Whereas humans just take, take, take and take. We harvest natural resources and turn them into poisons that we spread out into the world, killing natural wildlife and destroying habitats of wildlife.
Think of the impact that cutting down a 150 year old tree has on the future. We're becoming more and more efficient at harvesting materials from the wild but a lot of what we take won't be replaced for decades or centuries after the people that used those resources have died. We're destroying areas of the world that have been a certain way for thousands of years for temporary benefits or simple pleasure and not worrying about the future of the humans that will inhabit the world that we're destroying. There's a fucking mass of plastic in the ocean the size of Texas for fucks sake that isn't being cleaned by anyone because it's not financially beneficial to anyone right now.