Secular society badly misunderstands the terms chastity and celibacy. They think that a person who is not currently sexually active is “celibate”. And they think that a chaste marriage must be one in which the spouses do not have sexual relations. Wrong!
The Catholic use and understanding of those terms is as follows.
Chastity is sexual purity according to one’s state of life. For an unmarried person, chastity means avoiding all grave sexual sins, which of course prohibits all sexual acts. For married spouses, chastity means restricting sexual activity to natural marital relations open to life. All marriages should be chaste.
Celibacy is the renunciation of marriage for religious reasons, usually by means of a vow. Celibacy always includes chastity.
A single Catholic, who chastely avoids sex outside of marriage but is open to the possibility of marriage in the future, is not celibate. Most priests, almost all Bishops, any unmarried deacons, as well as all nuns and monks, take a vow or promise of celibacy; they have each renounced even the possibility of a future marriage.
The Church has always had some married priests. The Apostle and first Pope Peter was married at one time. (It seems that his spouse died prior to his calling by Christ.) The first Letter to Timothy says that a Bishop should be “the husband of one wife”, meaning not only that he must not have multiple spouses, but also that he must be faithful to his wife (single-hearted in devotion to his marriage). Some bishops in the early Church were married. And this implies that some priests and deacons were also married.
The Catholic Church in the East still permits some married men to become ordained as priests. But a single priest is not permitted to seek a wife. The priesthood is a higher calling than marriage. One can progress from a lower calling to a higher calling. But one should not regress from the higher calling of the priesthood to the lower calling of marriage.
A celibate priest has more time and energy to devote to the Church and the spiritual needs of the faithful. He can travel wherever God wills him to go. He can embark on a missionary journey. He can respond to a spiritual crisis in his flock with round-the-clock attention to their souls.
A married priest must split his time between family and parish. He cannot ignore his wife and children in order to devote himself fully to the needs of the parish. When there are many priests in the Church, having some married priests is acceptable. But it is always a compromise permitted due to the hardness of hearts of the faithful.
Jesus was chaste and celibate, so as to devote Himself fully to His high calling: to be the priest of our salvation. An ordained Catholic priest lives “in persona Christi”. He is a living image of Christ the High Priest. So it is always better for a priest to be celibate.
The Church can and does permit some married men to become priests: because we are all weak and mortal human beings, fallen sinners. But combining marriage and the priesthood is not the ideal. And since Jesus was chaste and celibate, the Church lacks the authority to choose a priesthood comprised solely or mainly of married priests.
Consider also that the Blessed Virgin Mary was chosen by God to be married and bear a child — yet she was also ever-virgin. Virginity and celibacy are better than marriage. Sinful secular society considers sexual enjoyment to be one of the highest goods. Christianity does not.
CANON X. If anyone says that the marriage state is to be placed above the state of virginity, or of celibacy, and that it is not better and more blessed to remain in virginity, or in celibacy, than to be united in matrimony; let him be anathema. (Council of Trent)
The Church might soon permit more married men to become priests. She should not permit single priests to seek a wife, unless (and very unfortunately) they resign from the active ministry. The Church cannot and will not have a priesthood that is entirely or mainly comprised of married priests.