Lucius Accius nailed it first, though it's been often attributed to Caligula, "Let them hate, so long as they fear."
And make no mistake, they ("they" being the rest of the college football world, not just the SEC) do both hate and fear Alabama. Deep in the recesses of their hearts, they also respect us, though they would never say that publicly. Otherwise, they wouldn't celebrate like frat boys on Bourbon Street on Fat Tuesday on the odd occasion that they actually win.
If you buy into the 1941 national championship, which I admit is iffy, it's been nearly 125 years (123 to be exact) since a child was born and didn't see an Alabama national championship before he or she became a 22 year old college graduate. If you don't buy into the 1941 NC, it's still been 78 years -- 1938.
And that's what scares them. Even in the odd weak periods, they know it won't last, and we'll be coming back way sooner than they would like to think.
We've won at an elite level in the 1920s, 1930s, 1940s, 1960s, 1970s, 1990s, 2000s, and 2010s. Notice that the only decades missing there are the 1950s and 1980s. Even then, we won SEC championships.
Truthfully, I don't think they really hate us. They deal with an envy that glows green like kryptonite by professing hate.
It's good to be envied or hated, or whatever they want to call it.