Your conclusion doesn't follow. Just because man didn't create it [1] doesn't mean that it's necessarily cyclical. The earth has changed in many ways in its lifetime. Some of those changes are indeed parts of cycles. Other changes are strictly one-way.
[1] hypothetically; I'm not actually making that claim, just following that line of argument
That's not to say that such a thing is without danger. I'm particularly wary of unintended consequences. But the people that are pursuing vast reductions in emissions aren't giving very much thought to the unintended consequences of their approach, either.
My point is that the arguments are being made with a huge amount of assumption on all sides. That's not the way to get to a good answer. We need to really consider what the likelihoods of possible outcomes are, in terms of lost human utility; and we might be able to do about them, including their costs and likelihood of success. I don't see a lot of real pro-vs-con debate - most of what I see is the Al Gore tactic of intentionally exaggerating claims to frighten people into acquiescence.
If it's anthropogenic then it is a brand new phenomena in geological time and will throw many ecological systems into disarray or destroy them completely because they never evolved the adaptations. If it's not anthropogenic, then no big deal this is a regular cyclical warm period that the Earth goes through naturally. If it's a natural cycle that we're not contributing to then we have nothing to fix.
What in the world does this have to do with asteroids?