Well, what I'm about to list are obvious, but here goes: it's historically one of the elite programs, at least while Wooden was there, 10 natties plus 1 from Harrick, more than any other school, recruiting should be easy in LA, deep talent pool, spotlights of LA, it would likely pay more, he's hot right now with how he put Dayglo in the national mix for BB, it's not the SEC, he gets away from a program with a shade of orange and UT as it's short title, he gets away from Bruce Pearl (his SEC kryptonite, as Frank Martin was at the Big 12), UCLA is down now and he's shown he can lift a program up from a low spot into at least an Elite 8 level.
That's enough, I guess.
Edit: well, maybe not enough.
There could be a bigger reason IMHO, but with some of the above as a backdrop. My recollection of his firing at Texas was that Patterson insisted he let go one or two of his assistants; Barnes refused and even offered to pay their salaries out of his own pocket; Patterson still insisted --- at least that's what I think I read about it all back then.
He was out of a job with hat in hand, and though I'm not suggesting that Dayglo took advantage of him, who knows what deal he got with them to sign on, and what his relationship is with Fulmer. But it sure seemed like he took the job but really wanted to stay at UT Austin.
Maybe that he's kind of hot property right now, even though 60+ years old, maybe UCLA is giving him a very wide berth in calling his own shots and might see this as his last chance in his career to either make or break his legacy. Maybe his discussions with UCLA (linked reporting suggests this has already happened) have given him a warm fuzzy and he would like to just "go West, old man" and give it a go. On his terms this time?