Yes, I deliberately said the doctrine.
As I have frequently pointed out to those who have questioned whether or not the Catholic Church should allow married priests, it already does allow them. Not only have the Eastern Catholic Rites always ordain married men (as well as celibate men), but there have also been exceptions in the history of the Latin Rite. The tradition of exclusively ordaining celibate men in the Latin Rite is just that – a tradition with a lower-case “t.”
It is a custom and, as evidenced by the examples I gave above, it can be changed. However, the people with whom I've communicated on this issue seem to remain confused about the status of the existence of a celibate priesthood. There will always be a celibate priesthood in the Catholic Church, and that is doctrine. Even if the Latin Rite made the decision ordain more married men within its ranks – which I believe would be a terrible mistake – it will never eliminate them. There has always been a celibate priesthood in all of the Rites of the Church. Its existence goes back to Scripture itself – Saint Paul was a celibate priest. Christ Himself, the preeminent and eternal High Priest of the Church was celibate. In other words, while the practice of exclusively ordaining celibate men in the Latin Rite is not a doctrine, the existence of celibate priests is. While the Latin Rite could change its exclusive discipline, it will not – cannot – eliminate celibate priests or, for example, decide to only ordain married men.
I've noticed two other important areas of confusion in regard to the celibate priesthood.
First: Many of those with whom I've communicated think that a change in this rule will allow priests to get married. This is not correct. While the Church has always taught that marriage is a holy calling, it has always taught that being called to serve God by serving the Church while living a celibate life as a higher calling. Again, we have the testimony of Saint Paul to back this up. You see, marriage imposes holy obligations on the spouses. These are so serious, that Saint Paul affirms that a married priest must divide his obligation. The celibate man, on the other hand, can devote himself exclusively to serving God through His Church. He can be moved where ever the Church needs, even remote or dangerous places, without having to be concerned about how it will affect his wife and children.
Because the priesthood is a higher calling to a greater good, it is permissible to impose the higher obligation on top of the lower one (marriage). Even then, the obligations of marriage are so holy that this is not to be done lightly and requires the consent of the wife. However, because the priesthood is a higher calling, it is not permissible to impose the obligations of the lower obligation on top of the higher one.
In other words, while a married man may become a priest, a priest may not get married. In fact, if a married man becomes a priest and his wife dies, he may not remarry. Additionally, the Tradition (note the capital “T” indicating that this is not a custom, but a doctrine that cannot ever be changed) of the Church is that while a married man may be ordained to the priesthood, only celibate men may be elevated to the rank of bishop.
Second: The reason given for pushing the idea of allowing married priests is that it will solve so many of the Church's problems – especially that of the shortage of priests. However, the only available evidence contradicts this assertion. If a man is not called to the celibate life before entering the priesthood, how will he handle being required to be celibate for the rest of his life if his wife dies? For this reason, at some points in the Church's history, the Latin Rite still required a commitment of celibacy for spouses when married men sought ordination. The man would become a priest and the wife would become a nun. The Eastern Rite never had this requirement, according to my studies, but they have been the first to defend the Latin Rite's practice of the celibate priesthood when the issue has come up. Additionally, if you look at the other religions that allow the equivalent to married clergy, they have many of the same problems. Clearly celibacy is not the real problem and does not cause the problems that are there.
Would allowing married men to become priest solve the problem of the priest shortage? No. As I stated above, if a man was not called to the celibate life when he entered the priesthood, will he accept the prospect of living the rest of his life as a celibate if his wife dies after he is ordained? I'm sure there are those who would, but the priesthood is a permanent thing. A man cannot simply change his mind about being a priest in the future.
If we look at the Latin Rite Catholic seminaries today, there is a striking observation that can be made. The seminaries that are full, that have waiting lists, that have been steadily growing, are typically those that adhere to what is today called “Traditional Catholicism.” Communities and orders that require the traditional disciplines, the traditional habits (clothes), and use the traditional Latin rites, still have a great appeal. Despite the world's assurances that the traditional structure and discipline of these communities will drive away young Catholics – that they are only for the older Catholics who pine for the “good old days” - these communities are being filled with young Catholic men and women who express joy over being able to serve God through His Church within these very traditional communities.
As Saint Paul says, not everyone is called to the celibate life, but God provides for the needs of His Church, so there will always be celibate priests, and monks, and nuns. The world will rail against their presence because it cannot believe that anyone can accept such a life, let alone be happy with it. The Church cannot dispense with them, ever. They have been part of the Church since her foundation, and God will always provide for her needs.
So, don't be fooled by the headlines taking the pope's words out of context. Yes, the discipline of an exclusively celibate priesthood in the Latin Rite of the Church can be relaxed. There are already exceptions to that discipline, but that does not mean there is going to be any wide-sweeping change in the practice. However, the existence of a celibate priesthood has always been part of the Church, it has always been taught and defended throughout the Church's history, it is part of her doctrine, and doctrine – by definition – can never change.