TL;DR It's from the movie Creed 2
Back in 2022 the night before the Tech game in Ames the team watched Creed 2. There is a workout montage of Creed, the boxer, stepping into the ring and the trainer, Rocky, throws down a tire, tells both fighters to step into the tire and don't step out until one of you gets knocked out. Both fighters being in close proximity doesn't allow for the big haymaker type knock outs, you have to sit there and take body blows while outlasting your opponent.
That became the mantra of the McGuire era, the other team is going to make plays, there are going to be bad calls, you're going to get hurt and banged up, the ball isn't going to bounce your way, but you need to keep your foot in the tire, take the body blows and outlast your opponent. The next day after watching the movie an assistant went out and bought a tire in Ames, Tech players held it up on the sideline to symbolize outlasting your opponent. Tech won the game and have used the tire off and on to hold on the sideline to motivate the team when things are not going their way to take the body blows and outlast.