It used to be how Hollywood did business. The studio would pair an established star with a rising ingenue to see if they have chemistry. If it worked, they’d make more films together. When the young star got older, they’d pair them with a younger star, and the cycle would continue. They did it with Humphrey Bogart and Lauren Bacall as well as Gregory Peck and Audrey Hepburn. They also did it in 1991’s Point Break with Patrick Swayze and Keanu Reeves. Swayze had already shown what he could do physically in Dirty Dancing and Road House. At the time, Reeves had only played burnouts in movies like Bill and Ted’s Excellent Adventure and Parenthood, and had never been a proper leading man. In the Hollywood of old, they’d put those stars together, and we’d spend two hours waiting for them to kiss. In Point Break, sadly, they never do.

Reeves plays Johnny Utah, a former college football player who joins the FBI and begins stalking a group of wild-eyed surfers he believes might be California’s prolific bank robbers. Their leader, Bodhi (Swayze), is the philosophical type. He speaks of living for “the ride” and liberating himself from societal expectations. He’s probably just an adrenaline junkie with delusions of grandeur, but once Johnny catches his first wave, he starts to buy into the mythology. He falls hard for the ocean and Bodhi. On the page, maybe they’re just supposed to be kindred spirits or even good buddies, but with each actor possessing an inherent softness, their connection feels more like a romance. I don’t know. Maybe it’s just the way the moonlight glances off the ocean.

The romantic undertones of Point Break weren’t noticed at the time, despite the fact that Swayze tells Reeves at one point, “You want me so bad you can taste it.” It’s not subtle, but Johnny does have a girlfriend (Lori Petty) who he claims to love, so maybe that confused audiences in 1991. He has a partner, too, a wise old war vet named Pappas who is played by a pre-meltdown Gary Busey. Johnny is coupled up three times over in Point Break, but it’s Bodhi who owns him. Johnny may be an arm of the law, but Bodhi sees the crazy in his eyes and cultivates it, taking him surfing, skydiving, and eventually bank robbing. Is it a strategy to implicate Johnny in his crimes and keep the law off his back? Or does he simply want Johnny to be his best and most liberated self? Yes. Point Break is a film of dualities (“Utah, get me two!”). Its irreconcilable nature is the essence of its charm.

It would, however, be entirely defensible if you were in it for the thrills. Bodhi takes Johnny to the edge, and we join them. Director Kathryn Bigelow, who would go on to win Oscars for 2009’s The Hurt Locker, stages every kind of sequence you’d expect from a ’90s action movie, but each has the flair of the original. An FBI raid turned shoot-out features a naked woman beating the crap out of our hero, and Anthony Kiedis (of Red Hot Chili Peppers) getting his foot blown apart in gruesome fashion. A foot pursuit through the houses and alleys of Los Angeles culminates in Bodhi picking up a snarling dog and throwing him at Johnny. Then there are the skydiving scenes, which have no cinematic antecedent and fully immerse the viewer in the thrill. It’s the ultimate bonding experience for the characters, but it bonds us to them, too, grateful as we are to be taken along for such a transcendent ride.

But mostly the thrill is between Swayze and Reeves, two actors whose talents were dismissed at the time and for too long afterward. Hollywood tried to fit Reeves into the leading man box, and his ill-fated attempts at playing normal humans set his reputation back a ways. Finally, he figured out he fits best into the dream worlds of The Matrix and John Wick. Swayze’s physical approach to acting was largely dismissed by the critical elite, but Dirty Dancing and Road House, which have both been mined for a sequel and a remake, remain indelible. Each brings a touch of zen, and no small amount of femininity, to their portrayals of alpha males. It was genius of Bigelow to let them revel in each other’s presence. Whether on a board, in the air, or on land with their bodies coiled somewhere between anger and lust, they create a rare chemistry in Point Break. The only shame is they never got to do it again.

Point Break (R, 122 minutes) screens at 7 p.m. on May 24 and 9:15 p.m. on May 25 at AFI Silver. silver.afi.com. $13.