Well, according to Hodge, the reason he hasn't been picked for Australia in recent years is that: "Six years ago, when I was 31, I was told I couldn't play for Australia again because I would not make the World Cup ODI side in four years. I wish the current selectors were around then because now it seems that form, not age of whatever, is the key to selection." (Herald Sun)
Whatever the reason's, as far as his cricket is concerned (especially in ODI cricket), he has been incredibly stiff. The last time he was in the Australian ODI side, he was in atrocious form, like Shaun Marsh is now in the test side, but instead of letting him go back to domestic level to get his form back, before being re-instated in the Australian team, they kept picking him, basically throwing him to the wolves.
That was the one time I was wishing they wouldn't pick him, as he was in pretty much career-worst form. But they kept picking him, when it was obvious he wasn't going to make a run and if they were looking for a reason to be able to not pick him again (if there were personality clashes, or whatever), they played it perfectly, picking him when he was out of form, so that they could at least say "well we gave him his chance and he blew it".
Then, a couple of years later, he gets into the very best form of his career and over the course of a couple of seasons makes hundred after hundred in the one dayers, putting him head and shoulders above anyone else at that level, in that comp, yet he doesn't get another chance, even when there were genuine openings.

That is stiff, especially when you consider there was a World Cup up for grabs at the time he was making so many runs. Maybe by then they didn't want to make the call to tell him he would be playing in the comp they said he wouldn't be a chance of playing in 4 years earlier. Wouldn't surprise me. And lets not forget, it was Hilditch and co picking the team. The same ones who picked Phil Hughes to play in the Ashes last year when he was averaging around 11 in the current Shield season and picked Steve Smith in pretty much every game Australia played in. There is a reason pretty much everyone in the country wanted them sacked from their selection duties.
As for those that reckon it must be his personality, or that he is hated by those in the teams he plays in, etc, I doubt that is a big issue, if at all, at least these days, when you consider what the likes of Hayden said about him, or what those in the commentary box for his games on Foxtel say about him.
On Foxtel, the likes of A.B., Greg Blewett, Damien Fleming and Mark Waugh sound genuinely bewildered when they watch Hodge smash yet another century and talk about why he isn't getting a look in for Australia.
Surely if he was in fact hated by all, word would have gotten around and the likes of them would be very well aware of it, and they would just go quiet when talk of Hodge potentially playing for Australia came up, or they just wouldn't bring it up to begin with. But it's usually the exact opposite. And when they interview him before, during, or after games, they usually have a great time and a laugh with him. If he was such a "knob" they wouldn't want to have a bar of him. But it appears to be the exact opposite, as it does when they talk about Hodge's time in the commentary box with them. They seem to genuinely enjoy his company and I'd say there's no way in hell they would want him anywhere the commentary box if he is in fact a "prick", that is "full of himself".
Even if he was those things, as someone said here yesterday, you ought to be professional enough to overcome little issues like that and do your JOB, if you're in a professional sports team.
I know it's not sport, but you could argue that in music you have to actually be closer and more in synch than those in sports teams, yet you hear on a regular basis about those in bands absolutely HATING each other, yet when they go into the studio, or on stage (where you have to be/perform more as a "team" than those playing cricket, for instance) they're able to perform at an incredibly high level.
Think Fleetwood Mac (just about all of them), during Rumours, The Rolling Stones (Mick v Keith), The Eagles (Don Henley v Glenn Frey), Oasis (the Gallagher brothers say hello!), Guns N' Roses (Axl v just about all of them), The Police (Sting v Stewart Copeland) and the list goes on. You even hear about bands where some of them in it have full-on fist fights during the songs in their concerts, yet are able to still perform well.
If they were all able to come together for the greater good, and kick massive amounts of ass, I'm pretty confident those in the Australian cricket team could have played cricket with Brad Hodge and been professional about it, especially when they're getting paid as much money as they were and are supposed to be grown up.