From a distance, from outside the circle of fans and aficionados, NFL football is both confounding and enraging. It is America's most popular sport and it is also deliberately, unspeakably violent. It is a particular kind of violence that is less about accidental collisions, adrenalin-fuelled fistfights or even a singular articulated blow. Football violence is wrapped up in machismo, militarism, swagger and patriotism. It isn’t a sport that thrives despite the violence but because of it.

The life of any professional athlete can be brutal but football players endure broken bones, torn ligaments and traumatic brain injuries as a matter of course, simply by doing the job they have been highly paid and contracted to do. These injuries are not bad luck or lapses in conditioning — although both can certainly play a part; they are simple facts of the game.

Football is a particularly American sport, although it certainly has fans in other countries, notably in Germany, Britain and Canada. But the NFL does not have the sort of international rosters that one finds among the nation’s baseball and basketball teams. There is no American football World Cup. Football is America’s violence.

The violence of football was in sharp relief on Monday evening when Buffalo Bills player Damar Hamlin collapsed in cardiac arrest after a tackle. The horror on the faces of the other players was profound. Hamlin appeared to have survived one of football’s routine collisions unscathed only to suddenly be in a critical condition.

Hamlin’s accident was grievous and rare. Still, it was a reminder of the punishing ecosystem of football, one that is unlike any other sport. Violence is such a central organising factor that except under the most ghastly circumstances, it goes mostly unnoticed. In football, players are helped off the field with damaged knees, bruised skulls and injured shoulders with some regularity. But if they can manage a thumbs-up or a wave to the fans, everything is deemed fine. The game will pause for a commercial break and then resume, as if nothing has happened. As if it’s not a big deal that a human being had to be carried away on a stretcher in the middle of a sporting event. As if every football game doesn’t tempt fate in a way that basketball or soccer or hockey do not.

In football, the players wear their helmets and pads to provide them some protection. But all that gear is also a recognition that the game is, in fact, predicated on men injuring other men. They give each other a bruising. They put a hurt on each other. They go to war.

The players are practically unrecognisable underneath all that protective armour, which society has learnt is not nearly as protective as it needs to be. It gives the players broader shoulders and more bulging muscles. It gives vulnerable men the appearance of invincible giants. And that is irresistible because part of the attraction of any sport, after all, is in watching competitors seemingly defy human limitations. Audiences are mesmerised by basketball players who appear to leap beyond the bounds of gravity, gymnasts who can soar through the air as if they have wings, tennis players who can spin, pivot and smash a tiny ball across a net with grace, power and precision. And with football players, there can be a balletic majesty in catching a pass mid-stride — eyes glancing back, forward and seemingly everywhere at once — and hurdling over obstacles and on to victory.

But that ballet is performed against a soundtrack of bones colliding against bone, of air being squeezed out of compressed lungs under the weight of a pile of opposing players. What is so captivating about men ploughing into each other? Is there another sport in which violence is so elemental?

Boxing, of course, is a blood sport. Fighters fine-tune their body and sharpen their minds before a match. And when they are at their finest, they move with extraordinary speed and precision, their blows landing so quickly that their power is only understood by what is left in their wake: a swollen jaw, a bruised torso, a teetering opponent. Boxing is often called the sweet science, which alludes to the idea that a successful boxer is one who combines fearlessness, technique and an ability to anticipate an opponent’s moves. It is a bit of soothing poetry to soften the coarseness of the sport, to distract from the broken noses and bloodshed. Mostly, though, boxing has always been honest about its ugliness.

Football is not so much wrapped in poetry as it is patriotism, not the small-town county fair version, but big-city capitalism. Football benefits from the lucrative economics of machismo. It markets and sells live action, superhero violence. Fans of professional football like to call players warriors and gladiators, and equate that with bravery and toughness while forgetting that warriors all too often are gravely wounded and gladiators often fought to the death.

Americans love their football. They are loyal to their favourite teams. Fans admire football players' athleticism, their impressively complex tactics and the competitive spirit of a Super Bowl. But in the past decade, much of the romanticism that once surrounded football has disintegrated to more clearly reveal the racism in the corporate offices, the sexism within the culture and the enduring physical pain of the game. All that’s left is the violence.

And Americans settle into their seats for that. They tailgate in anticipation of this volatile pastime. This orchestrated pummelling of another team, the walloping of another person. The winner’s victory is a violent one.

• Robin Givhan is senior critic-at-large writing about politics, race and the arts. A 2006 Pulitzer Prize winner for criticism, Givhan has also worked at Newsweek/Daily Beast, Vogue magazine and the Detroit Free Press