Some teams just don't have as many reasons to hate other schools. You have to look at tradition, competition, geographic location, and historical moves to fully understand where a fan base is coming from.
No doubt, LSU-Ole Miss is a rivalry, and based on tradition, LSU's most hated opponent is Ole Miss. Any LSU fan I've ever talked to claims Ole Miss to be the "traditional" rival. However, because Auburn and LSU seem to compete for the Western Division every year now, not to mention the competitiveness of each game they've played the last several years, the game is considered bigger than a seemingly meaningless match-up with Ole Miss (which surprisingly enough has been a lot closer than people realize the last few years). Recent moves and the history that they become will play an important factor on the shape that the LSU-Alabama game takes over the next few years. But for now, Ole Miss is still LSU's biggest rival.
Arkansas has the unfortunate situation of being a team that joined the conference long after the 10 members that have made up the conference during the modern era. The LSU-Arkansas "rivalry" is just the SEC's way to give each team a "rivalry bowl," much like the Egg and Iron. Only thing is, these teams don't have a long standing tradition of playing each other, nor are they remotely close to one another. Sure, their state borders touch, but Fayetteville is the same distance from Baton Rouge as Knoxville, and is further away from Baton Rouge than any other SEC town except for Lexington and Columbia. In essence, that game means about as much to LSU fans as the game against State does. And I'd say based on geography and history (recent history) Arkansas's biggest rival in the conference has to be Ole Miss right now. Even if Rebel fans don't really care.
Based on tradition, geography, history, etc...Ole Miss has every right to claim State and LSU as rivals, much like we claim Ole Miss and Alabama. With these two Mississippi teams, who you hate more probably has everything to do with where you grew up, experiences you had in Oxford, Starkville, Baton Rouge, or Tuscaloosa, and more relevantly, how those teams have performed recently in each sport. I hate Alabama about as much as I hate Ole Miss not only because Alabama fans live in the past, act like bitches, etc.. but because I love basketball almost as much as football, and because I grew up near the AL-MS state line, where there's about as much Crimson as there is Dixie.
State fans: Are you mad that Ole Miss has more rivals than us? Well, they do. But all that means is that more people hate them than us. And that means we're more likable than them. At least that's how this State fan is choosing to look at it. The bottom line is both State and Ole Miss fans should be glad that we have deep, significant rivals to begin with, and appreciate the importance (although meaningless in the grand scheme of things) that we place and subsequently argue over all year long...
It's college football, baby. And soon enough, it'll be all over us.