One good biblical argument for celibacy (for those called):
I say to you, whoever divorces his wife (unless the marriage is unlawful) and marries another commits adultery."
[His] disciples said to him, "If that is the case of a man with his wife, it is better not to marry."
He answered, "Not all can accept [this] word, but only those to whom that is granted.
Some are incapable of marriage because they were born so; some, because they were made so by others; some, because they have renounced marriage for the sake of the kingdom of heaven. Whoever can accept this ought to accept it."
The teaching of the Catholic Church would take a bit to unpack, but as I understand it:
Priestly Celibacy is a teaching or instruction, not a doctrine or dogma.
Deacons may be married, but are not allowed to remarry after their wives die.
You're right that ministers of other Christian denominations can continue in their vocation as a priest, while married.
But that's not an argument for anything. For one thing, priests need to be chaste in order to perform their duties at Mass. They need to be free to perform their duties completely selflessly without needing to care for their families. The top down structure of the Church means that a parish community will be assigned a priest, not a parish community will raise up a priest, like they might in another tradition.
In short, for diocesan priests it wouldn't be fair to the wife to be subject to the Bishop with her husband. It wouldn't be fair to the parishoners to come second to the wife and children. For priests in various religious orders, they mostly take vows which include Chastity (which is not exactly the same as celibacy, but in this sense it is). Those vows come out of monastic traditions reaching back to the 5th-6th Century.
More info from Catholic Encyclopedia