Ryan made the comments Tuesday at a breakfast with Texas delegates to the Republican National Convention, in a room where with many people who had backed Texas Sen. Ted Cruz for the nomination.
"Conventions can be pretty darn exciting sometimes," Ryan said, a day after anti-Trump delegates protested on the convention floor. "We've got really big problems in our country. And in our party we've had, let's just say, a really big family discussion."
He then turned to college football, explaining how important it is when a team advances to a big postseason game, fans of other teams in its conference root for it to win.
He discussed how intense the rivalries are in the Big 12, the conference of the Texas Longhorns and Texas A&M Aggies, whose supporters in the room whooped and hollered.
"Boy, those rivalries are tough, especially when the Big 12 was the Big 12 and you guys were at each other's throats," said Ryan.
But he said, "When one of the teams advances to a big bowl game or a national championship, don't you root for the Aggies if you are a Longhorn?"
The crowd booed no.
"You don't? This whole riff was not worth it," a deflated Ryan said with a smile. "My entire premise has just been obliterated."
Ryan then explained how things are different in Wisconsin, where once the hard-fought regular season is over, Badgers fans throw their support to a rival for the broader good of the conference -- inferring that Republicans who didn't vote for Trump in the primary should support him now.
"I come from Big 10 country, so we fight like heck against Ohio State or Michigan, and then when it doesn't go our way or they make it to the Rose Bowl or they go to the National Championship, we root for them because we're in the same conference."
Ryan implored the delegates to take a Big 10 approach to football and politics. "Good grief. Holy Moly. This explains everything right now," he said.
Despite the missed analogy, the Texas delegation warmly embraced the new speaker. He got standing ovations on his way in and out of the room.