Erhm, if humanity manages to survive to the year 10000, your argument is extremely invalid.

Well, if we can start colonizing other planets we're basically good to go. It'd be really hard for humanity to destroy itself once we've spread out to multiple systems, since the complete destruction of one world would still leave the others doing fine.

If we can survive the next thousand years or so, I think we're good. Unless a supernova in our area of the galaxy happens, and then we're dead. But it wouldn't be our fault, at least.