As I understand it, Feynman's tentative explanation for why ice is slippery (which he himself qualified with "they say") has since fallen out of favor. This isn't to quibble with Feynman -- if anything, the point he alludes to here and emphasizes in a lot of other works is that science is a continuing process, always updating itself, and individual scientists are not prophets or oracles.
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 electros...
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: