First is that the Pac12 doesn't consider BYU to be enough of a major research university. Its primarily a 4-year university and even though it has some amazing postgraduate programs, a majority of students are done in 4.

Another and less talked about reason is social/political. The Pac-12 doesn't want a team that discriminates against certain communities. Religion being a key driver for some of those policies means that BYU won't budge on those policies and the Pac-12 won't either. Especially when it comes to LGBT topics.

Bonus reason - BYU makes a LOT of money by being independent. They don't have to deal with TV contract arguments or having to pay a conference. On a good season, the variety and strength of schedule fill seats.