While Cyclops and Wolverine have been frenemies for years, often because of their different leadership styles and their competition for Jean Grey's affections, the two X-Men reached their absolute lowest point in the 2011 comic-book crossover event X-Men: Schism. Years of pent-up aggression and old grudges resurfaced as the two came to blows in a violent, no-holds-barred brawl. This shaped the future of Marvel's Merry Mutants for years to follow, and Scott Summers and Logan became bitter enemies instead of friends and allies.
Leading up to the story, the X-Mansion had been destroyed during the events of X-Men: Messiah Complex. This resulted in the Children of the Atom relocating to an island dubbed Utopia off the coast of San Francisco as new mutants began to mysteriously reemerge across the planet after the cataclysmic events of Decimation. The X-Men and Hope Summers welcomed the latest mutants into their ranks, including the teenager Oya. Meanwhile, Wolverine led a new iteration of X-Force that proactively responded to threats to mutants around the world, openly employing lethal force to ensure the fragile future of the species.
At the start of the story, Cyclops and Wolverine appeared as unified as they had been in years as they faced off against a resurgent Hellfire Club led by its new Black King, Kade Kilgore. Nearly overwhelmed, Cyclops and Wolverine reached their first big falling out when Wolverine urged Oya to run to safety before Cyclops convinced the young mutant to use her powers to wipe out a detachment of Hellfire Club soldiers. Wolverine was haunted by the psychological toll putting his young clone X-23 on X-Force took on her. This coupled with becoming a surrogate father figure to Oya led to Logan's vocal misgivings about Cyclops' willingness to use the younger mutants to employ lethal force.
The last straw between the two would finally snap when the Hellfire Club sent a massive, experimental Sentinel to attack the new mutant community on Utopia. While Wolverine felt Hope, Oya, and the younger mutants should take cover or retreat from the incoming doomsday machine, Cyclops allowed them to join the battle, putting their lives at risk. Desperate and frustrated, Wolverine threatened to blow up Utopia to force the young mutants to retreat rather than fight. This led to Cyclops and Wolverine reminding each other of their past grudge over Jean Grey's love, resulting in an all-out brawl between the two men, despite the Sentinel continuing to lumber towards the island.
Ultimately, the Sentinel was destroyed, but the rift between Cyclops and Wolverine was irreparable. Wolverine led a detachment of X-Men that disagreed with Cyclops' leadership to found a new school for young mutants back in New York while Cyclops continued his hard-line agenda on Utopia, echoing Professor X's rift with Magneto. This culminated in Wolverine siding with the Avengers during Avengers vs. X-Men after Cyclops refused to relinquish Hope to Earth's Mightiest Heroes in order to divert the Phoenix Force. Cyclops was branded a mutant terrorist and went on the run, and he and Logan never fully reconciled before the line-wide relaunch of Dawn of X, where their friendship was restored.
Schism represented the lowest point in the relationship between the two superheroes as desperate times led them to have wildly different perspectives about the best way to forge a new future for the mutant race. During what should have been a unified front when mutants were poised for a rebirth following Messiah Complex and Avengers vs. X-Men instead led Cyclops to become more of an antihero than a committed superhero. And while it's still unclear if the events of the 2011 event will have any impact on the current state of Dawn of X, a renewed conflict between the two men remains a distinct possibility.