On the one hand it's supposed to be competitive, attract millions of pounds in sponsorship, and be performed by people trained to within an inch of their mental and physical limits.
And on the other it's supposed to be friendly and nice and you can take your children to watch it and any little problem can be resolved with a handshake because everyone involved is as honourable as the younger son of an earl.
It's why in rugby men built like meat-tanks twist one another's testicles off in order to get a squashed ball up their end of the pitch, but think it's impolite to tackle 'too early'.
It's why in tennis two gladiators smash a rubber ball around for hours in matches on which millions of pounds can hinge, dispute every line call or chuck rackets around in a tantrum then shake hands at the net like they're Fred Perry.
And it's why we call 22 testosterone-crazed social delinquents running about in the mud while being paid a million pounds a second 'The Beautiful Game'.
It's not beautiful. It's the most expensive failed attempt at care in the community we've ever had. Half the Premier League should be kept away from cutlery, never mind given the wherewithal to purchase supercars and thrash them up and down the M60.
Yet we fall off our sofas with shock when a highly-paid, over-trained, genetically-lupine footballer in the shape of Luis Suarez takes a bite out of a rival player's arm. What were you expecting? He probably eats raw kittens for breakfast and ravages the countryside at full moon. If all he left on Branislav Ivanovic was bite marks it is, in the world of professional sport, little more than playful banter.
And yet there were millions of fans watching, and plenty of children who saw it even if the ref didn't. It's not the way to carry on off the pitch, and should no more be acceptable on that patch of grass than it is in your back garden, local park or school field.
The fact that it is seen almost as an unavoidable part of that football match means that it could and will be seen the same way in football matches played where the goals are made of jumpers and the teams consist of only a few friends.
But if it did happen anywhere else the police could get called in, or at the very least some parents. The biter would be left in no doubt that is not how you play the game and they'd be lucky to find anybody who wants to play football with them for a while.
Suarez has had a ticking-off from his club and fined an undisclosed amount of money, which is a maximum of around £200,000 and probably much less. The cash has gone to the Hillsborough families' charity and will no doubt be put to better use by them than it would by a player who demonstrably has more money than sense.
Part of the reason football inspires so many people is the fairytale it weaves - of dirt-poor children like Suarez, who grew up playing barefoot in the streets of Montevideo, achieving stardom and wealth by dint of skill and talent.
But fairytales always have a dark side, and that is the fair punishment of people who do wrong. From Snow White's stepmother eating her own poisoned apple to Red Riding Hood's wolf being chopped up by the woodcutter, there is always justice, and it is always equal to the crime.
Yet in sport there is no such thing. Actions which off the pitch would see someone arrested go unquestioned, even though millions have seen it and there's video available from every possible angle. Ivanovic says he doesn't want to press charges - that wouldn't stop the police doing so in any other situation.
There is arguably more evidence for assaults committed under the cover of a game than there is for almost any other crime, yet they are rarely, if ever, prosecuted, and rarer still achieve a conviction.
This Sunday not only did Suarez assault someone in plain view of millions, but in Bahrain Sergio Perez apparently rammed McLaren teammate Jenson Button while the two were driving at 186mph.
They were only competing for fifth place, and they're on the same side; it's silly, but on any other patch of tarmac it would be dangerous driving and carry a maximum penalty of two years' jail and a year's disqualification for the very good reason they could both have died, and worse taken some bystanders with them.
You can put it all down to the competitive nature of sport if you like, but on exactly the same day 36,000 people competed against themselves and each other to complete a physically gruelling race and they all managed it without intentionally assaulting anyone else.
A chap in a wheelchair collided accidentally with a lady from Ethiopia, but that was as serious as it got and neither party bared their fangs or racially abused one another, despite the fact they'd both put in years of training and plenty of sponsorship and kudos rested on their success.
So what does it show, if some people can take part in a sport without acting like thugs and others who we make more of act like crack addicts who've heard Delia's just recommended their favourite rocks for making gravy and the middle-classes are panic-buying all the supplies?
First, that paying top sportspeople millions gives them a sense of invincibility even greater than that bestowed by the adoration of fans and their own towering egos, and that fining them the equivalent of a small house in the Midlands is as effective as docking a petulant teenager thruppence from his pocket money.
Take an arm and a leg, as Suarez would, or don't bother.
And secondly that if you want people to be well-behaved, regardless of their wealth, sport, training or place of origin, the best way is for them to know that they are just like everyone else in society and liable to get arrested if they bite, thump, stamp, ram or otherwise commit a foul whether it is on the track, the pitch, or the street outside.
If they are allowed to commit crimes in some places, there's nothing stopping them or the people that slavishly follow them committing them anywhere else.
You can't dismiss it as being 'part of a contact sport' when all of life is a contact sport, and the rest of us manage to get through it without taking a pound of flesh out of someone else's hide.
Because if the police's jurisdiction stops at the side of the pitch then people will expect to stop elsewhere too.
At the castle gates, for example.