The top reason people hate Alabama and have hated Alabama really differs according to audience:
Fans of other SEC schools hate us because we have been so dominating for so much of the history of the conference. While the performance of teams isn't necessarily a zero-sum game, the results are and we've been a virtual monopoly for many of the years of the SEC.
Fans of schools from other conferences don't universally hate us, but the supporters of many of those schools don't have much love for us because many of our bowl victories rudely ended once-in-a-lifetime seasons for them and we sometimes were quite non-chalant or even disappointed in playing their team. That made their losses even more unpalatable.
Many reporters and sports announcers don't seem to like us simply because we play boring football and yet we are very successful and prevent many of their more exciting and entertaining teams from getting the spotlight. I'm not sure why many of them released so much vitriol when Saban came to Alabama other than they sensed that once again boring, defensive-minded football would be dominating the high-flying circus acts that they prefer to cover. It's understandable why the Miami press was so peeved since they had their pride destroyed by losing a high-profile coach to, of all places, a redneck state. They consider themselves some cultural mecca and the mere thought that someone would prefer Alabama to Miami made their finely-manicured nails curl.