I don't think his explanation for why a chair pushes back on your hand is quite right, either. I've mostly been told that material solidness comes from the Pauli exclusion principle, not electrostatic repulsion.
I don't know quantum mechanics, so I don't have a good perspective on the problem, but the electrostatic explanation has always seemed lacking to me. The electric charge in a neutral atom is fairly well-approximated by a symmetric sphere of negative charge with a bunch of positive charge at the center, so two atoms shouldn't experience much electrostatic repulsion until their electron clouds overlap. At which point [I've heard] the PEP should dominate the electrostatic force.
Can any physicists or physics students comment?
Pauli exclusion holds neutron stars and atomic nuclei apart. ie. much denser than atomic contact.
Even with the clouds overlapping, I think it's mostly electromagnetic. They are too sparse for exclusion to be significant.
To get any deeper, we would need someone who understands the source and mechanism of exclusion.
I thought this video was a really good question dissolving by Richard Feynman. But it's in 240p! Nobody likes watching 240p videos. So I transcribed it. (Edit: That was in jest. The real reasons are because I thought I could get more exposure this way, and because a lot of people appreciate transcripts. Also, Paul Graham speculates that the written word is universally superior than the spoken word for the purpose of ideas.) I was going to post it as a rationality quote, but the transcript was sufficiently long that I think it warrants a discussion post instead.
Here you go: