I'll begin with the confession that I have no special insight into what may be worth backing when they go under starter's orders tomorrow, though even those of us who seldom bet are tempted to have a punt when it's such an important race.

I refer, of course, not to the Cheltenham Festival, but to the even more exciting run-off in the Sistine Chapel. When the Master of Papal Liturgical Celebrations says "And they're off" (though the words he uses are "extra omnes"), the cardinal-electors will begin choosing the new Pope.

The Cardinal Archbishop of Milan, Angelo Scola (2/1) and the Ghanaian Cardinal Peter Turkson (4/1) lead the field, but the bookies' odds – which are usually better than opinion polls for political contests – are more often than not unreliable in this race. For example, Paddy Power currently has "Peter" as favourite (6/4) for the next Pope's choice of name. In fact, that is the one name more or less certain not to be adopted by whoever emerges as the next pontiff, partly because nobody has presumed to do so since St Peter, and partly because of the (fraudulent but persistent) Prophecy of the Popes attributed to St Malachy, which predict Peter will be the name of the last Pope.

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But that is a fairly piffling example of the way in which worldly assessments of the workings of the Roman Catholic Church are so often at odds with the Church's view of itself. There are others far more out of kilter.

The announcement of Pope Benedict's retirement sparked the usual commentary about new directions which the Church could or should take under his successor. That was predictable enough, and indeed more comprehensible than in any previous papal interregnum, because of the novelty of a Pope retiring, and because of the seriousness for the Church of the growth in allegations of abuse (and, which may be worse, concealment of that abuse).

It would be difficult to overstate the importance of tackling such issues, which must involve genuinely determined attempts to be more transparent; it should also require that, in potentially criminal cases, the Church refers matters to secular authorities rather than trying to handle them internally. It is even possible to imagine that the discipline of celibacy could be reconsidered – something that, before his own accelerated resignation, Cardinal Keith O'Brien had thought of as a possibility.

There are other issues, however, which many progressive critics of the Church (both within and outwith it) raise which suggest they have failed to grasp the most basic points about the institution. Those who argue that a new Pope ought to reconsider traditional teaching on contraception, the ordination of women, divorce, sexual behaviour – gay or straight – outwith marriage, and all the rest of it; who say, in short, that it is time the Church came to grips with the realities of the modern world, are failing to understand some central points about its teaching.

The Church is not interested in adapting itself to the modern world; indeed, it is, on one level, not interested in adapting to the world at all. Instead, the Church is, by its own definitions of itself, in the business of adapting the world to be more like the Kingdom of Heaven. Nor, to the disappointment of quite a lot of liberal theologians and commentators, does it imagine that the Kingdom of Heaven runs along the lines which might meet favour with, say, a leader-writer on The Guardian.

There are, of course, a good many Christians who do not share the Roman Catholic Church's position on such matters. But while any Anglican can disagree with the Archbishop of Canterbury (most of them do) and any Protestant, almost by definition, provide his or her own interpretation of Scripture in balance with their consciences, Roman Catholics, up to and including the Pope himself, are bound by the magisterium of the Church.

Indeed, John Paul II ruled that neither he nor any other Pope had the authority to ordain women – to take the example which seems most anachronistic and unfair to most people, Christian or not, who do not subscribe to traditional Catholic teaching. His doing so was actually an instance, not of the Bishop of Rome making a ruling which was infallible as an ex cathedra statement, but of pointing out that the ordinary and universal magisterium (ie, the historic teaching of the Church) was itself infallible, and incapable of contradiction, even from the Pope.

The marriage of clergy is merely a matter of Church discipline; indeed, there are already a fair number of married Roman Catholic priests, since the establishment of the Ordinariate for former Anglicans who have jumped ship to Rome.

It is likely that the majority of people think the Catholic Church's position on many of these issues is wrong. But it does not follow that they can expect the new Pope to change its teaching simply because they are incompatible with received bien-pensant nostrums.

Nor can I quite see why atheist critics, who think it absurd that anyone should believe in the literal truth of the Resurrection, or believe that the doctrine of transubstantiation can be disproven by sticking the host under a microscope, would nonetheless expect the Church to operate in accordance with the equal opportunities employment code of Tower Hamlets Local Authority.

The next pontiff has the great challenge of ensuring that the Church puts its house in order over abuse cases – and is seen to be doing so. He will also have to do much to overcome many people's outright hostility to the institution he leads. Those are more than enough to be going on with.

But it is delusional for those outside the Roman Catholic Church to imagine that any organisation dedicated to furthering the Gospel is ever going to conform to the norms of the secular world. For outright opponents, that may well count as part of the case against it.

To expect that the next Pope will operate like the CEO of a company, though, is to miss the whole pint of what he is for. The irony of speculating about which candidates the cardinals will tomorrow try to choose between is that, in the words of one of them, their job is not to choose at all. The Holy Spirit has already chosen; the cardinals merely have to work out what the choice is. Even without the smoke, the urn and the embroidered ballots, that's not your typical HR selection process.