That ordination to the priesthood forever marks a man was universally believed until the rise of Protestantism in the 16th century. The Church has always lived Hebrews 7:17 (“You are a priest forever, according to the order of Melchizedek”). Only after Protestants criticized the ordained ministry did the Council of Trent solemnly define that it is divinely revealed that every priest is a priest forever. Today, when priests are released from the obligations of the priesthood they do not become laymen again. They are simply given permission not to exercise the duties and obligations of the priesthood. They remain priests. No priest is ever “laicized,” despite the popularity of that unfortunate word.
In 1976, the Congregation for the Doctrine of the Faith noted in its decree Inter Insignores that the Church had no authority to ordain women because Christ himself did not choose women to be among the Twelve and because the apostles, who were given authority to teach after Christ ascended, never chose women either. Rather than being explicit in Scripture, it’s a necessary logical conclusion from the revelation of Scripture and tradition.
Christ was not subject to cultural norms. The apostles, who taught more than Christ could in his earthly life, adopted many Greco-Roman customs instead of Mosaic norms. The Greeks had priestesses, but the apostles still did not ordain women. With the approval of Pope Paul VI, the Congregation for the Doctrine of the Faith declared that these facts were definitive: the Church cannot ordain women.
In 1994, Pope John Paul II reaffirmed this conclusion in Ordinatio Sacerdotalis. A year later, the Congregation for the Doctrine of the Faith noted that the saintly pope’s letter was declaring that it’s always been taught that women can’t be ordained. There may come a day, as happened in the 16th century, when a pope or an ecumenical council must solemnly declare that this is a divinely revealed truth, but for now, it’s part of the ordinary and universal magisterium that we must believe women can’t be ordained lest we become dissenters to the Catholic faith.
Celibacy is in a different category. Although the fourth chapter of the Gospel of Luke tells us that St. Peter had a mother-in-law, the Lord’s counsel in favor of virginity for the sake of the kingdom (Mt 19:12) became normative. St. Paul noted that unmarried men are entirely devoted to the affairs of the Lord (1 Cor 7:32). Celibacy was the discipline very early on.
Although there were local councils as early as the fourth century, such as the Council of Elvira, which mandated the celibacy of priests, it was understood that even married priests were practicing sexual abstinence because they were to be single-minded in the worship of God. It was a carryover from Judaism, which understood that priests serving in the Temple ought to abstain from sexual relations with their wives to keep themselves focused on God.