In order to prove him wrong, you'd have to really grapple with the question of how to have a self-sustaining ecology in space. This is something I basically never see in online space boosterism, and note that empirical attempts to answer it like Biosphere 2 ended in complete failure (and those were on Earth, which is orders of magnitude easier).
Now sure, the politics on who and what gets to go to thr next world will doom many. But physics can alleviate the whole "we'll tear each other apart over 200 years of space travel" part
I think more likely is we figure out wormholes. If we can't go light speed we can instead fold space like a piece of paper and reduce the space we need to Traverse. That may or may not be as easy as FTL.
I obviously don't have the finer details in line.
The other problems may become more amenable - one just can't know what will happen. Amazing things like CRISPR - an incredible tool that lets us edit genes - appear suddenly and change everything.
Sequencing a Genome once seemed a massive task and now it's no big deal - so perhaps some of these problems will end up like that.
We can also re-engineer ourselves and that might help a lot.
- Increased lifespan making the trip possible in 1 generation - A hollowed out asteroid or other extremely large biosphere. It is not hard to imagine something large enough to overcome the ecological problems - Virtual reality (the holodeck) if you're still worried about social issues in a large space. BTW, most teens today would be happy to stay in a closed room, as long as they had a phone. (I exaggerate, but only a little)
All of these things are reasonable extrapolations of existing tech. In 200 years, I'm sure a whole lot more will be possible.
Understatement of the year.