Idk about you, but when I hear "bear down", I think of someone being constipated. I also struggle with the cat/bear conflict here. It turns out it is of fairly random origin - maybe there's more to the story somewhere else...

"John B. Salmon (Button Salmon) was the student body president, as well as the starting quarterback for the Wildcat football team and the catcher for the Wildcat baseball team, and member of Sigma Nu fraternity and #12 in Chain Gang Junior Honorary, now known as Links Junior Honorary.

"The day after the first game of the 1926 football season, Salmon and two others were involved in an automobile accident, in which their vehicle flipped over in a ravine. Although Salmon's friends were not injured, Salmon suffered a severe spinal cord injury. In the aftermath of the accident, football coach Pop McKale visited him in the hospital every day. During McKale's last visit, Salmon's last message to his teammates was, "Tell them.. tell the team to bear down."