It can be seen from two aspects - Political and Religious:

Political - the bishop of Rome as he was called then did not want the priests family inheriting his wealth so by letting priests not get married this was solved.

Religious - that the priest is married to the Church, and should be at her disposal at all times.

However, eastern rite catholic churches who are schismatics form the orthodox church and keep the traditions and beliefs of the orthodox church but accept the primacy of the pope over the orthodox church can get married.

Clergy members of other churches that were already married and convert to Catholicism can still stay married.

This however is rejected by the orthodox church putting it in simplistic terms is that because it can led to other sins such as homosexuality, masturbation, adultery, etc...

Another Answer:

The tradition of priestly celibacy is only mandatory in the Roman (Latin) Rite of the Catholic Church. There are numerous other rites within Catholicism that are in full communion with the Bishop of Rome and are thus Catholic. Some of these other rites allow married men to enter the priesthood. After their ordination however they are not allowed to marry.

For a list of the rites of the Catholic Church see the link below.

In Catholicism, it has to do with tradition. In the Latin Rite, the Church has a tradition of not allowing married men into the priesthood. There are certain exceptions to the tradition, if a married and ordained Anglican or Lutheran priest wants to minister in the Catholic Church, then he will be allowed to remain married and be ordained a Catholic Priest.

It is the tradition of the other "Eastern" rites to allow married men into the priesthood. Though once a person is a priest they cannot marry, in any rite, unless they leave the priesthood. Though it is very uncommon in the United States, especially because many believe that Catholic priests can't be married at all.

Answer In the early days of the Catholic Church, the leaders ended the practice of priests marrying in order to stop the property, money and land of the church from being "inherited" away from the church. That is, from priests leaving money and land to wives and children when they died. If a priest was never married, then he had no family to leave anything to, therefore all the wealth accumulated by the church would stay in the Church.

Answer Catholic priests aren't allowed to be married because they are to be celibate- (abstain from sex)

Answer They are married to God!

In the Orthodox faith, priests can be married BEFORE they are ordained, but not afterward. Bishops must remain celibate.

Catholic Answer Priests have not been allowed to marry for the entire history of the Church. In certain eras of the Church's history there has been some abuse of this and that is why the regulations named above were later put into effect. But there is ample evidence from the very first centuries that priests were never allowed to marry in the Latin Rite. In the Latin Rite, to be ordained to the diaconate and priesthood, men must take a vow of celibacy, which is a solemn promise to God that they will not attempt marriage. Priests are "another Christ" and thus are trying to live the life that He did as perfectly as possible. One of the things that they give up "for the kingdom" is a normal married life. This is a discipline of the Church, not a doctrine, and it is freely entered into by any man that is seeking ordination in the Church. In some rare instances, a man may already married when he is ordained, or in the eastern Rites, he is allowed to be married before he is ordained. However, all priests take a vow of celibacy upon ordination and if he is already married, he may not remarry if his wife dies.

Answer:

Although Catholic priests of the Eastern Rites may be married before they are ordained, if they are unmarried at ordination they may not marry afterwards; this is the Eastern tradition which is also held by the Orthodox. Married Latin (Roman) Catholic men cannot become priests, as the Latin branch of the Catholic Church requires celibacy as a sign of total dedication to Christ and His people. However, by way of exception, if a married Protestant or Anglican clergyman joins a (Roman) Catholic he can become a Catholic priest while still being married; however, when his wife dies he may not remarry. His wife must give approval for her husband to become a Catholic priest.