This answer is mainly a Catholic perspective on both Traditions.
What is common to both Traditions?
What is common to both Traditions is that celibacy is required for all those who are called to be bishops. Now this is interesting because it saying that there is something about being a bishop that requires the celibate state.
According to Catholic teaching the bishops enjoy the fullness of the priesthood. Therefore the fullness of the priesthood in both Traditions require celibacy, and therefore, there is something about being a priest and the celibate state.
Does scripture help make a connection?
To Jesus' Teaching about Divorce, the disciples reacted by saying that it would be expedient not to marry, to which Jesus replied:
“Not all men can receive this precept, but
only those to whom it is given. 12 For there are eunuchs who have been
so from birth, and there are eunuchs who have been made eunuchs by
men, and there are eunuchs who have made themselves eunuchs for the
sake of the kingdom of heaven. He who is able to receive this, let him
And the footnote explains:
19.11-12 Jesus means that a life of continence is to be chosen only by those who are called to it for the sake of the kingdom of God.
A lit bit later, after the episode of the Rich Young Man Jesus replies to Peter’s question:
And every one who has left houses or brothers or sisters or father or
mother or children or lands, for my name’s sake, will receive a
hundredfold, and inherit eternal life.
Therefore scripture speaks of a life of continence and the renunciation of houses … or children chosen only by those who are called to it for the sake of the kingdom of God/the LORD’s name.
Therefore the understanding of celibacy for priests from the Church’s perspective is that with the priesthood there comes with it not only a renunciation of the married state, but also a renunciation of what is allowed within the married state i.e. marital relations i.e. the calling is to a life of continence. It will be good to note here that Jesus' teaching applies not only to priests but to others as well e.g. virgins, widows and widowers, monks, even lay persons, as evidenced in the history and life of the Church.
From just these scriptural passages, it is easy to see that if an unmarried suitable male candidate is called to the priesthood, he of course cannot be ordained and later marry. But if he is married, and then called to the priesthood [as some Apostles were] then it is a renunciation of houses … or children for the sake of the kingdom of God/the LORD’s name.
But why a life of continence for priests?
In his Directions concerning Marriage St. Paul says the unmarried state being a gift from God just like the married state, is better. Later in the same chapter he goes on to says of the unmarried that they:
1) are anxious about the affairs of the Lord, how to please the Lord, and
2) how to be holy in body and spirit, and
3) that what he says is for their benefit so that they can secure their undivided devotion to the LORD.
This is what the Church and her saints have also echoed, that this gift from God of a life of continence for the sake of the kingdom of God/the LORD’s name is so that those called may serve the Church and souls indiviso corde, i.e. with an undivided heart.
But if this applies to all the unmarried, why the priests?
In St. Paul directions concerning marriage mentioned above, even the married are called to periods of continence. Why? So that they may devote themselves to prayer. This is the key: it is all about the LORD. Explaining:
Christ is unmarried but he is a groom, actually the Bridegroom of his Body, the Church. Needless to say, the wedding is coming [cf. Scripture and those who understand the Jewish roots of the Church and the meaning of “Truly, I say to you, I shall not drink again of the fruit of the vine until that day when I drink it new in the kingdom of God.”]. Can the priest then, who, according to the Church acts in “persona Christi” marry whilst they are wedded to the Church or can the unmarried first marry and then go on to be wedded to the Church?
It should be noted that the LORD speaks of the future in the resurrection [where] they neither marry nor are given in marriage, but are like angels and the saintly Pope St. John Paul II [the Great] in his General Audiences on Theology of the Body teaches that The Kingdom of God, Not the World, Is Man's Eternal Destiny, therefore a life of continence in the LORD is the destiny of those worthy of the resurrection. Therefore those who have received the gift from God of a life of continence for the sake of the kingdom of God/the LORD’s name are already a sign living here and now of the life of those who will be worthy of the resurrection.
These then are the reasons and theological underpinnings of the requirement of the life of continence for priests.
From a Catholic perspective, the departures from this either within the Catholic Church herself or the within the Orthodox Tradition are just that, departures, either as exceptions or as accommodations or as aberrations.
From the foregoing it is wrong to view this as the "Church forbidding someone" or "someone being forbidden". From the LORD, his Apostle to the Gentiles, and the Church, this is a gift to be received from God of a life of continence for the sake of the kingdom of God/the LORD’s name.
A closing comment from the Church’s Jewish roots
It should be noted that in the OT that God required some of his prophets to be celibate or live a life of continence or observe a temporary period of continence and all of these were in circumstances and matters connected directly to him.
This is the something: Why the image [union of man and woman] when there is the real thing [Union of God and man/Christ and his Church]?
Endnotes & Materials Source:
1) Stickler, Alphonso M. Cardinal (Vatican Archivist) The Case for Clerical Celibacy : Its Historical Development and Theological Foundations. San Francisco: Ignatius Press, 1995. This work covers both Eastern and Western traditions.
2) Priestly celibacy in patristics and in the history of the Church by Roman Cholij, Secretary of the Apostolic Exarch for Ukrainian Catholics in Great Britain.
3) The Ancient Tradition of Clerical Celibacy by Mary R. Schneider | Catholic Culture.
4) The Truth About Priestly Continence and Celibacy in the Early Church | Unam Sanctam Catholicam.
5) The Orthodox Churches and priestly celibacy by Damaskinos Papandreou, Orthodox Metropolitan of Switzerland.
6) The biblical foundation of priestly celibacy by Ignace de la Potterie, Biblical scholar.
7) Interview With Theologian on the Foundations of Celibacy (Married Priests Will Always Be an Exception) | ZENIT.
8) Priestly Celibacy by Matt1618.
9) According to Midrash and Aggadah after the Giving of the Torah, a life of sexual abstinence was imposed on Moses due to his spiritual standing.