Before moving to Utah, I thought it was just a funny thing Mormons pretended to make a big deal out of for fun.
When I got here, I realized based on the perceived culture at BYU, Utes legitimately hate BYU. And to be fair, it's based on how they've been treated by a certain type of Mormon their whole lives.
But the fact that they're the little brother comes mostly from them being more obsessed with BYU than most BYU students are with them.