Pope (Emeritus) Benedict XVI, in his 2010 book, Light of the World, explains why the Church sees homosexuality as incompatible with the priesthood, even for those who live a chaste life, insofar as “…their sexual orientation estranges them from the proper sense of paternity, i.e., from the intrinsic nature of priestly being.”
Actually, his words are worth quoting at length:
“Sexuality has an intrinsic meaning and direction which is not homosexual. The meaning and direction of sexuality is to bring about the union of man and woman and in this way give humanity posterity, children, future. This is the determination internal to the essence of sexuality. Everything else is against sexuality’s intrinsic meaning and direction. This is a point we need to hold firm, even if it is not pleasing to our age. The issue at stake here is the intrinsic truth of sexuality’s significance in the constitution of man’s being. If someone has deep seated homosexual inclinations—and it is still an open question whether these inclinations are really innate or they arise in early childhood—if, in any case, they have power over him this is a great trial for him, just as other trials conflict other people as well. But this does not mean that homosexuality thereby becomes morally right. Rather it remains contrary to the essence of what God originally willed.
Homosexuality is incompatible with the priestly vocation. Otherwise, celibacy itself would lose its meaning as a renunciation. It would be extremely dangerous if celibacy became a sort of pretext for bringing people into the priesthood who don’t want to get married anyway. For, in the end, their attitude toward man or woman is somehow distorted, off-center, and, in any case, is not within the direction of creation of which we have spoken. The Congregation for Education issued a decision a few years ago to the effect that homosexual candidates cannot become priests because their sexual orientation estranges them from the proper sense of paternity, from the intrinsic nature of priestly being. The selection of candidates to the priesthood must therefore be very careful. The greatest attention is needed here in order to prevent the intrusion of this kind of ambiguity and to head off a situation where the celibacy of priests would practically end up being identified with the tendency to homosexuality.” (pp. 151-3)