Fr. Donald Cozzens argues against it, with what I consider a weak argument, the gist of which is:
The church even holds that marriage (including spousal lovemaking) is a sacrament -- something sacred that contributes to the sanctity of husbands and wives. In light of this official teaching, it is dawning on many Catholics that mandatory celibacy for priests, a canonically imposed discipline of the church, is precisely that -- a discipline.
They are asking, "How is it that a discipline of the church has been allowed to trump a sacrament of the church?" In effect, the church is saying that should God call a man to the priesthood, God will not, at the same time, call that individual to the sacrament of marriage. It's right to ask, how does the church know this?
Public opinion surveys indicate that most Catholics, priests included, believe the discipline of celibacy needs a serious review. Recently the retired archbishop of New York, Cardinal Edward Egan, observed that obligatory celibacy is open for discussion. It is not, Egan noted, a matter of dogma.
First of all, truth is not determined by public opinion or a vote (thank goodness). Second, just because the history of the Church (and don't forget the present - with Eastern Catholics) allows for married priests, means that it is a good idea for it to be part of the universal Church. Third, because sex is "good" does not mean it has to happen all the time for everyone. In fact, the sacrifice of giving it up is made greater because it is something worthy of sacrifice.
Even as we reverence everything that God has made, we must let go of everything that God has made, precisely for the sake of God.
This is why, as G.K. Chesterton noted, there is a tension to Christian life. In accord with its affirmation of the world, the Church loves color, pageantry, music and rich decoration (as in the liturgy and papal ceremonials), even as, in accord with its detachment from the world, it loves the poverty of St. Francis and the simplicity of Mother Teresa.
The same tension governs its attitude toward sex and family. Again, in Chesterton's language, the Church is "fiercely for having children" (through marriage) even as it remains "fiercely against having them" (in religious celibacy).
Everything in this world -- including sex and intimate friendship -- is good, but impermanently so; all finite reality is beautiful, but its beauty, if I can put it in explicitly Catholic terms, is sacramental, not ultimate.
In the biblical narratives, when God wanted to make a certain truth vividly known to his people, he would, from time to time, choose a prophet and command him to act out that truth, to embody it concretely.
For example, he told Hosea to marry the unfaithful Gomer in order to sacramentalize God's fidelity to wavering Israel. Thus, the truth of the non-ultimacy of sex, family and worldly relationship can and should be proclaimed through words, but it will be believed only when people can see it.
This is why, the Church is convinced, God chooses certain people to be celibate. Their mission is to witness to a transcendent form of love, the way that we will love in heaven. In God's realm, we will experience a communion (bodily as well as spiritual) compared to which even the most intense forms of communion here below pale into insignificance, and celibates make this truth viscerally real for us now. Though one can present practical reasons for it, I believe that celibacy only finally makes sense in this eschatological context.
I think Fr. Barron easily wins, but with one caveat. He forgot his audience and his argument will be lost on many who read it, because there are few sound bites.