The Latin priest, and many of the Eastern Catholic priests, model their lives on Jesus Christ, who was celibate.
"His disciples say unto him, If the case of the man be so with [his] wife, it is not good to marry. But he said unto them, All [men] cannot receive this saying, save [they] to whom it is given. For there are some eunuchs, which were so born from [their] mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive [it], let him receive [it]." - Matthew 19:10-12
Though it is not "forbidden" for the clergy to marry in the Christian religion, it is strongly recommended that one does not marry, if one is to be a priest or minister. I have read how Protestant minister's families have interfered in their religious duties. A Catholic priest does not have these concerns and can give God's work first priority.
Well, I agree that there are Protestant ministers that are not necessarily following the leadership qualifications. Because in addition to saying "the husband of one wife", the passages in 1 Timothy 3 (as well as Titus 1) indicate that they need to be "one who rules his own house well, having his children in submission with all reverence (for if a man does not know how to rule his own house, how will he take care of the church of God?)."