I know your question was posted a long time ago and the thread wnet into all sorts of directions but I would like to say a few words about your original question, in the hope that it could maybe address it directly.
You are right that the electric repulsion between the electrons of your body and of the chair play a major role (btw, electron degeneracy pressure does not play a role in that context, as others have suggested, because the average separation between the elctrons is far greater than their typical deBroglie wavelength. The pressure is simply not large enough).
However, your answer should lead you to another obvious question: but the electrons in the atoms should be strongly attracted to the nuvclei, which have positive charges. So what keeps all the electrons from collapsing to the nuclei in the first place? The answer is Heisenberg's uncertainty principle. *This* keeps the electrons away from the nuclei,which is why there is a chair to support you. Even if you assume that the electrons around nuclei have some angular momentum keeping them stable on orbits (like the planets around the Sun), once you would sit on the chair you would expect that the push created by your electrons on the electrons on the chair (and vice versa) would provide an additional force that *would* make the elctrons fall toward the nuclei (as would happen if some giant external force would suddenly give a push toward the Sun to the planets). The elctrons cloud *do* get distorted a bit and "squeezed" but, once again, the HUP comes into play and keeps the electrons from falling toward the nuclei.
(there is a few complications to this admittedly crude explanation. But I won't get into those unless there are questions).
I am pretty sure this is what that physicist had in mind in introducing the HUP in that context. That's my guess, anyway.
Pat