Beilein felt underpaid/unappreciated: While few people are going to turn down more money, it doesn't appear that a low salary was the cause of the departure. According to multiple sources, West Virginia offered Beilein at least as much money as the Wolverines did. Beilein has also never appeared to be chasing money in his various job dalliances. With everything else being equal, including salary, wouldn't he have stayed at West Virginia, where postseaosn prospects for the next couple of years are much brighter?
His family doesn't like Morgantown/West Virginia: This one continued to hang on, and be centered on Beilein's wife Kathleen, despite several denials. While it might not have held the same appeal as Richmond, Va., it did not appear to be a huge factor in the decision to leave. Ann Arbor may be fine, but there's certainly nowhere in West Virginia that compares to some areas around Detroit.
The buyout clause chafed at his sense of control: This seems be a contributing factor. West Virginia's final offer apparently included a quicker reduction of the buyout clause, which could have put him out from under it as quickly as two years from now. Beilien certainly viewed it as a shackle that kept him from investigating some other jobs, and sorely wanted it removed from his current West Virginia deal. His new contract at Michigan reportedly does not include a buyout, which leaves the Wolverines vulnerable to his whims (wonder what might happen if Billy Donovan takes the Kentucky job), but will certianly make him happier.
Beilein believed he couldn't recruit well enough to win a national title at West Virginia: There's no doubt that Beilein was frustrated with his ability to attract five star recruits for even a visit to WVU. Like any other coach, he thought that if he won enough, the gates would eventually open. But while he was able to sign underrated players like Da'Sean Butler and Wellington Smith, his classes still included a number of players that didn't get a lot of publicity. While WVU fans would be the first to point out that Beilein's M.O. is to get the most out of underrated players, he has to wonder what he would be able to do with top rated recruits.
Well, he's going to get that chance, at least in theory, because Michigan, and the Detroit area, is loaded with top prospects. However, in order to get them, Beilein will have to dive headfirst into the sometime shady world of AAU basketball. To a degree he has never done before, Beilein will have to deal with AAU coaches and directors, or face the wrath of many associated with the Michigan program. How he fares in that task might be the biggest single factor in determining how his Michigan career plays out.
Facilities improvements: While Beilein certainly wouldn't have turned down a basketball practice facility, and did want more room for the program as a whole, this issue didn't appear to be a substantive part of his decision to move on. West Virginia was making more room for the basketball program at the Coliseum, as the Physical Education department is slated to move out at some point in the future.
The five-year cycle: Is it mere coincidence that Beilein's last three coaching stints have lasted five years? Probably so. However, when the coach says that it was a "gut feel" that it was time to move on, you have to wonder if that same feeling popped up five and ten years ago as well.
In the end, the only person who really knows why Beilien took the job is Beilein himself, and he's not talking. Nor, given his nature, is he ever likely to. Although it's likely that some combination of the above reasons came together to make Beilein feel that the move to Michigan was a step up and not sideways, we'll probably never know the final story.