Is it the word homo that's homophobic?
It is indeed. 'Homo' is a homophobic slur. For example:
Three large, anti-gay slurs had been tagged on the couple's car in red spray paint: HOMO DIE, FAG and FAGET (sic).
More like with the intention of using a short form.
Gay is shorter word than homosexual. Polly deliberately used a homophobic slur. While we expect that kind of thing from him (or at least we do here, when he writes under his real name he never writes such things), it's a real pity that the mods have decided to let him get away with it yet again.
It's like saying 'Rich' is an offensive way of calling Richard.
I'd point out the clear flaw in your claim but of course to you there is nothing wrong with calling a Pakistani a "paki", not that you would be so brave as to call any of them that to their face, or even within their hearing.
Once again I find myself wondering why he is (still) so fascinated by 'homo's.
No you don't: it's completely obvious why he thinks about gay men so often.