These enabling technologies are very, very hard. No doubt about it. That's why we can't do this today, or even a century from now.
But the physics show it's possible and suggest a natural evolution of capabilities to get there. We are a curious species that is never happy to keep our present station in life and always pushes our limits. If colonizing the solar system is technically possible, we'll do it, sooner or later, even if it takes hundreds or even thousands of years to get there.
> I like how you treat "the fusion problem" with a throwaway, "Yeah, we'd have to solve that" as if we just haven't sufficiently applied ourselves yet.
If you'd read my comment, you'd see I didn't say that. Fusion rockets would help, but we don't need them. Nuclear pulse propulsion or fission fragment rockets could conceivably get us to the 0.01-0.05c range, and the physics is well understood.
> And even if we solve the issue of accelerating a human being to acceptable speeds to reach another star, the next closest star is 4 light years away. That means light takes 4 years to reach. Even if you could average half the speed of light, that's 8 years, one way. Anything you send is gone.
Getting to 0.5c is essentially impossible without antimatter, and we have no idea how to make it in any useful quantity. Realistically, we're going there at less than 0.1c, probably less then 0.05c. Nobody who leaves is ever coming back, and barring huge leaps in life sciences, they probably aren't going to be alive at the destination either. It'd be robotic probes and subsequent generation ships to establish colonies. But if you get to the point where you are turning the asteroid belt into O'Neill cylinders, a multi-century generation ship starts to sound feasible.