Golf is said to be a gentlemen’s game with quiet swings, polite claps, and whispered respect. That vanishes when the Americans meet the Europeans in the biennial Ryder Cup matches. Rivalries and personal conflicts, combined with national pride, can lead to the type of chatter you hear before a boxing match.

This year the spotlight is glaring on two men: Bryson DeChambeau of Team USA and Rory McIlroy of Team Europe. Mr. DeChambeau, a YouTube influencer and two-time U.S. Open champion, threw down the gauntlet on Thursday, saying he would “love” to be matched against Mr. McIlroy during the 2025 Ryder Cup that begins Friday at Bethpage Black on Long Island.

“I think rivalries are good for the game,” Mr. DeChambeau said during his pre-tournament press conference. “I have ultimate respect for Rory as a player. It’s going to be fun to go up against him whether it’s directly or against other players. Would I love to go against him? Yeah. He’s fiercely competitive.”

Mr. McIlroy, a career Grand Slam winner playing in his eighth Ryder Cup, didn’t exactly downplay his interest in such a matchup. The heart and soul of Team Europe said, “All I want to do is go and try and put blue points on the board. I don’t care who it’s against. If I come up against Bryson at some point, I think that’s great. I think that’s wonderful for the championship and wonderful for us, as well, in some ways.”

It’s not certain the two rivals will play in the same match. The Ryder Cup is a team event where the first two days consist of two formats — four-ball and foursomes — with six matches each day, featuring teams of two. Captains select the pairings from their 12-man rosters. In four-ball, each player plays their own ball, meaning four balls are in play on each hole. The lowest score wins the hole for their team. The team winning the most holes wins the match and a point for their team.

In foursomes, sometimes known as alternate shot, the two players on each team take turns hitting the same ball. The team with the lowest score wins the hole, and the winner of the most holes wins the match and a point toward the overall score. The United States needs 14½ points to regain the Cup it lost two years ago at Rome. Europe retains the Cup in case of a 14-14 tie.

The competition isn’t decided until Sunday’s 12 singles matches, during which the golfers go head to head in a match-play competition. It would be dramatic theater if Messrs. DeChambeau and McIlroy dueled on Sunday with the Cup on the line.

The two high-profile golfers have taken jabs at each other since Mr. DeChambeau rallied to win the 2024 U.S. Open at Pinehurst after Mr. McIlroy missed two short putts in the closing holes. Their rivalry intensified at the 2025 Masters last April, when they played together in the final group and Mr. McIlroy emerged as the winner to claim the Green Jacket and a career Grand Slam.

Afterward, Mr. DeChambeau told the media Mr. McIlroy “didn’t talk to me once all day,” and later suggested “I’ll be chirping in his ear,” should they meet in the Ryder Cup.

Mr. McIlroy returned the fire recently, calling Mr. DeChambeau an attention-seeker. “I think the only way he gets attention is by mentioning other people,” Mr. McIlroy said. “That’s basically what I think of that. To get attention he will mention me or Scottie [Scheffler] or others.”

Team USA is captained by Keegan Bradley and led by Mr. Scheffler, ranked no. 1 in the world. But Mr. DeChambeau has been the lightning rod. The only LIV golfer on the American squad, Mr. DeChambeau has taken heat from broadcaster Brandel Chamblee, who called him “circus barker” who is an “odd duck” and a “captain’s nightmare,” who only cares about his YouTube channel.

Meanwhile, Team USA has openly embraced him, impressed that he attended team dinners at the Tour Championship at Atlanta and in Napa Valley despite being barred at the PGA Tour events being held there.

“I feel like Bryson could be like the difference for us in a strange way from the standpoint of feeding into these fans and the style of golf he plays,” Team USA’s Xander Schauffele said at Bethpage, adding, “This is his arena. If he views himself as a gladiator golfer, this is as good as it gets.”

Team USA is hoping Mr. DeChambeau will energize the galleries at Bethpage Black and enhance the Americans home course advantage. It’s a role Mr. DeChambeau welcomes. The last time the Europeans won on American soil was 2012.

“I couldn’t be more excited for the opportunity to get them riled up and excited for what’s to come,” he said. “Hopefully, I can hit some great shots when it matters most.”

One person sure to be rooting for Mr. DeChambeau is President Trump, who is expected to arrive at the Ryder Cup on Friday afternoon. Mr. Trump will be the first sitting American president to attend the Ryder Cup.

Mr. Trump is close to several of the American players, including Mr. Scheffler and Sam Burns. Mr. Trump is especially close to Mr. DeChambeau, appearing on the golfer’s “Can I Break 50?” YouTube series and also appointing him to the President’s Council on Physical Fitness.

Mr. DeChambeau said Mr. Trump’s presence will “inspire” Team USA. “I think he’ll be a great force for us to get a lot of people on our side,” he said. “I think it will be interesting and exciting to see how the crowd and everybody reacts.”

Team Europe, led by captain Luke Donald for the second straight event, is formidable, returning 11 of the 12 players that captured the Cup at Rome. The Europeans are 13-6-1 in the Ryder Cup since 1985.