Why can't Catholic priests get married?

First, the distinction. Celibacy is a discipline of the Latin (Roman) Church, not a doctrine. Eastern Catholic Churches ordain married men, and the Latin Church ordains married former Anglican and Lutheran clergy. Married deacons are common. So it could change, in principle. The Church keeps it because it is precious.

The reasons. Jesus was celibate, and He praised those who "have renounced marriage for the sake of the kingdom of heaven" (Mt 19:12). St. Paul, celibate himself, wrote that "an unmarried man is anxious about the things of the Lord, how he may please the Lord," while a married man is "divided" (1 Cor 7:32-34). The priest is configured to Christ the Bridegroom, whose Bride is the Church; his celibacy is a living sign that he belongs to her entirely (CCC 1579). It is also a sign of the world to come, where they "neither marry nor are given in marriage" (Mt 22:30).

History. From the earliest centuries the Church asked continence of married clergy; the Council of Elvira (c. 305) legislated it. Universal celibacy for the Latin Church was enforced by the reforms of the eleventh and twelfth centuries, but the ideal is apostolic.

Objections. Celibacy does not cause abuse; the vast majority of abusers in society are married or non-clergy, and celibate priests offend at rates no higher than other men. The priest shortage is real, but the Eastern Churches with married clergy face shortages too. The question is not whether celibacy is hard (it is) but whether it is a gift. Two thousand years of saints say it is.

A gift, not a loss. A celibate priest is not a man who gave up love. He is a man who chose to love everyone, and to be father to a parish rather than to one family.