Well, the thing is, if we don't colonize other planets, the mankind will go extinct very soon.
No. Even in a nuclear war, a few million people at the very least would survive.
But civilization wouldn't. And then we would have to start all over again. Nukes start flying, and you can kiss all this amazing technology goodbye.
That's still not the same thing as going extinct. And we wouldn't really go back to the stone age since we'd still know stuff, if you see what I mean. Even in the worst nuclear war, I'd wager that civilization would be repaired fully in 300-500 years at most.