When someone says a team in the rise... That is used generally as a comparison to their competitors. In the sec I would say ole miss and Ms state are currently on the rise. A&M and auburn were teams on the rise over the past couple of years. But compared to others in the sec I don't think you can put tn in that ''on the rise category yet''
There are two necessary components to a team being "on the rise". First, that they are improving (relative to their previous talent levels). Second, that they are becoming more competitive, or that they are improving at a faster rate than their competitors. Usually these two can coincide. However, it is possible to be improving, but also be in a conference full of improving teams, and it is possible to be creeping up on your competition *only because* they are getting worse.
It is inarguable that UT is on the rise in the first sense. We are definitely a more talented team than we have been in the past few years. And we are gaining yet another incredible class.
It is also hard to argue that we aren't improving faster than many of our competitors. First, we are definitely improving. So, the only way we aren't improving relative to our competition is if we are either so far away from being competitive that it doesn't quite apply, or if all of the teams in the SEC (or most of these teams) are improving as well.
Well, we definitely fit the first criteria - we are not so bad that we aren't competitive. It isn't unlikely that we are ranked entering next year, and we definitely will be with a couple of wins at the beginning of the schedule.
As for the second, most teams in the SEC are stagnating or declining. Florida is coming off of a few bad years, and while they lost their *****y coach, they are also bringing in (barring miracle) a terrible recruiting class. Vanderbilt is junk. Georgia is the same they always have been, but are losing Gurley and their QB. South Carolina is declining. Kentucky is improving, but at a slower and lower pace than we are. Missouri has improved, but I don't see that continuing. This appears to be their ceiling for the foreseeable future.
Out west, only Ole Miss and Miss. State are improving...but they aren't our immediate competition, and having a couple of talented and improving teams does not negate our being "on the rise". It isn't relative to all teams, but relative to most.