Its popes still preach that sex outside marriage is a sin, despite so many unmarried priests regularly having sex - much of it criminal.
For centuries priests married freely, but the church came to view women with suspicion - clearly it still does - and it slowly changed its mind.
Today priests must not marry.
But St Peter had a missus at the dawn of Christianity and it seems he coped, despite the distractions.
We know he was married because the Bible records Jesus curing Saint Peter's mother-in-law of a fever. It's not recorded if the first Pope thought that a good thing or not.
Clerical celibacy has been in the news as the Catholic Church - in Australia, across Europe, and in the Americas - wrestles with infestations of busy bisexual paedophiles who have been squeezing the sacraments in to hectic schedules of forced sex with minors.
Grudgingly and shamefully slowly, the church has been forced to act on the rapists in its ranks.
But the Catholic Church's priority has always been self-preservation; that gene is dominant in its DNA. I was reminded of that the other day by events unconnected with the findings of the state government report in to clergy child sex abuse.
The findings were bad enough. The Victorian parliamentary committee found in the church a rancid culture that trivialised the issue of clerical rapists, the exposure of whom was viewed as a "short-term embarrassment".
But it was the church's response to another issue that revealed its priorities.
Let's call it A Case of Two Kevins.
The first is Father Kevin Lee, once a popular priest in Sydney's west, who made headlines recently when he was swept to his death as Typhoon Haiyan crossed the Philippines where Lee had made his home with wife Josefina and their six-week-old daughter Michelle.
He made bigger headlines last year when, as the parish priest at Glenmore Park, and as chaplain to the NSW Police, he appeared on Channel 7 News admitting he'd broken his vow of celibacy and had been secretly married for a year.
He outed himself, he said, in the hope that other priests living a double life, perhaps seeing a another man, maybe a woman, but more likely abusing children, might do so themselves.
He hadn't broken any laws.
He hadn't killed anyone.
Indeed, he'd caused no harm at all, unless you accepted the church's view that his congregation was "traumatised".
Seven's news went to air at 6pm on May 1 last year with the report of Lee's admissions and claims of wrongdoing by fellow priests.
The Catholic Church went into shock.
This needed to be dealt with immediately.
It issued a press release within hours - also dated May 1 - explaining that Lee's authority to act as a priest was withdrawn.
An administrator turned up to take over his church at 8am.
In less than a day, this Kevin's case was closed.
By the end of the year Lee was laicised - defrocked.
Things moved much slower when it came to Fr Kevin O'Donnell, perhaps Australia's worst white-collared, black-hearted paedophile.
By at least 1958, the church was made aware that this Fr Kevin was a bisexual rapist with an uncontrollable lust for unlawful acts involving Catholic children in his "care".
Rather than act that day - as they did with the other Fr Kevin - they spent years covering up the crimes, moving this Kevin from parish to parish as he raped his way through generations of traumatised children, an unknown number of whom took their own lives.
Eventually, the law dealt with this Kevin and jailed him, albeit briefly.
He was released in 1996 and his maker made an appointment with him for March 11, 1997.
Let's be generous and agree it really was 1958 when the Catholic Church was informed about this Kevin.
Let's assume they heard this news that New Year's Eve.
That means the church perversely tolerated Father Kevin O'Donnell for another 13,949 days until God brought his commission to an end.
Two of O'Donnell's victims were the daughters of Chrissie and Anthony Foster. He attacked Emma as a child. She never recovered. Her short life was one of self-harm, addiction and anorexia ending in suicide aged 26 in 2008.
He attacked her sister Katherine - a girl he baptised - who also considered suicide, turned to alcohol and is crippled and brain-damaged after being struck by a car.
"When a priest marries a woman they take swift action, yet when a priest rapes a child nothing happens," said Chrissie. "It just shows they are more disgusted with a priest marrying a woman."
Chrissie reminded me of the evidence given at this year's inquiry by Archbishop Denis Hart when he was asked about twice jailed paedophile Father Des Gannon and why it had taken almost two decades for the church to act.
"Well, better late than never," Archbishop Hart said.
Perhaps those were the first words our second Kevin heard in another place.