But away from the arguments, what is it actually like to lead a life without having sex?
This is, we are told, a highly sexualised society.
In the 21st Century UK, indeed in almost all of the West, sexual imagery can be found in many places, and many young people expect to have a number of sexual partners before eventually settling down.
This perhaps may explain why the idea of a celibate lifestyle, as practised by the clergy of the Catholic Church, as well as adherents of other religions, causes a great deal of puzzlement among non-believers.
"In our sex-dominated society, people tend to view celibacy as a form of sexual anorexia - a sad and lonely state at best, unnatural at worst," says Elizabeth Abbott, author of A History of Celibacy.
Jimmy O'Brien was a priest for the best part of a decade before deciding he had to leave his vocation. He has now been married for 20 years to a woman he met while still a priest, and he has two children.
Born in Tipperary, Ireland, he started his training at 18. From a Catholic background, he completely accepted the idea of celibacy. But after several years as a priest in the south of England he began to change his mind.
"Accepting it was one thing and living it was another. Four or five years into it, it's only then the implications of the decision you made were questioned.
"It isn't so much the celibacy aspect, it is the loneliness. At 28 or 29 a lot of my friends were settling down and having children, my older brothers and sisters were having children. There was no significant other there for you."
By the time he was 34, Mr O'Brien felt he had to leave to preserve his "own personal sanity". Although he says he did not break his vows while a priest, he had already met his future wife by the time he left.
"By this stage I had kind of got myself into a relationship with a woman and was having to make that decision. It was a friendship that developed. When I did leave, the relationship I was in went onto a different level."
Even in slightly more conservative times, there have always been many for whom celibacy was not easily understood. Former nun Mel Baird encountered many baffled people in the late 1960s and 1970s.
"People thought I was completely mad," she notes, and there were some who made wild allegations - that she was just odd, a lesbian, or even not celibate at all.
"Some people couldn't understand it was possible to be fulfilled and to enjoy what you were doing without being sexually active. It didn't mean I wasn't a sexual being."
But the times were certainly different when Mrs Baird began training to be a nun in 1965.
"We are actually looking at quite a different climate. I had been brought up in a Catholic home in a Catholic school, educated by nuns.
"I never saw celibacy as a deprivation. I never denied my femininity. I was still a woman with the same feelings. It doesn't mean I wasn't interested in men or interested in having children.
"I saw my choice to become a nun as part of what I needed to do to achieve the whole. I didn't see it as an imposition."
And while the non-believer might be preoccupied with the idea of a constant battle against multifarious temptation, Mrs Baird had support.
"You had the whole back-up of a [convent] community, unlike priests."
When the nuns were tempted they were encouraged to "pray or to go and do something positive - it is about channelling that energy".
But Mrs Baird decided before taking her final vows that she was not destined to be a nun for life.
"I was beginning to wonder whether I was in the right place. At 26 I wasn't the same person I was at 18. I had experienced life. I had grown up. I no longer found it fulfilling.
"I would have become miserable. There is such a thing as a temporary vocation."
Serving priest Fr Stephen Wang - who has written on the subject - does not see celibacy as a privation.
"There are struggles. Times of loneliness; sexual desires; dreams about what marriage and fatherhood would be like. I don't think most of this is about celibacy - it's about being human."
Fr Wang sees practical arguments for celibacy, but is more moved by the idea that as a single person, Jesus and the parishioners have a central place in his life. And, most importantly, he is happy.
"You need affection and human intimacy. I've got some wonderful friends. I get home to see my family every couple of weeks. I escape to the cinema now and then. And I pray. Not to fill the gaps, because some of them can never be filled, but because the love of Christ is something very real and very consoling.
"I'm aware that it gives me a freedom of heart that is a unique gift. It helps me stay close to Christ, and draws me closer to the people I meet each day."
Neither Mrs Baird nor Mr O'Brien left their vocation to pursue a hedonistic lifestyle.
Both married and had children. Both are in professions that represent a continuity from the caring side of their previous calling - Mrs Baird has pursued a career in psychiatric nursing, while Mr O'Brien has worked with vulnerable children and now runs children's homes.
Both are still active and dedicated Catholics. Neither were condemned by fellow Catholics for the decision they made.
Mrs Baird does believe that those in a religious community, monks and nuns, should have to accept celibacy, or leave as she did. But she says priests should have a choice about whether to be celibate, at least in part to stop the church losing otherwise devoted clergymen.
For Mr O'Brien there is an argument for married priests as there is an argument for women priests, but from a personal point of view he would not necessarily have stayed as a priest were he allowed to marry.
"From a personal choice I don't think you would want to commit someone to living their life in a fish bowl."SIC: BBC