We're not in the midst of a great extinction event and even if we were it would not be the first one caused by a single species. Probably the first one was caused by the appearance of Cyanobacteria some 2.7 billion years ago which started to make use of sunlight through photosynthesis. A few hundred million years later the produced oxygen started seeping into the atmosphere and boom, nearly all anaerobic life on the planet was wiped out.

We are part of the ecosystem no matter how much you try to deny it. The planet will abide, humans most likely as well. If you want to call for fewer humans on the planet - something which seems to be the future anyway since births are rapidly declining almost everywhere - that's fine but realise you're just following others like Malthus who did so before. Malthus was proven wrong many times over, you will be proven wrong as well since if there's one thing humans are good at it is adapting to a changing environment. If it gets colder humans adapt, that's how we made it through the series of glaciations. If it gets warmer humans adapt, that's how we made it through e.g. the Roman and Viking age warm periods.