The Eastern churches and the Western church agree that there is an affinity between celibacy and the priesthood. The episcopal office is the fullness of the priesthood, and in all Eastern churches only celibates can be consecrated bishops.
The question is whether only celibates should be ordained to the priesthood. The Western church makes an exception and ordains some married men (former Anglican priests and Protestant ministers).
The call to celibacy is distinct from the call to orders. Newman, even when he was an Anglican, felt called to celibacy. The theory is that men are called to celibacy and the church chooses some of them to be priests. The reality is different: men feel called to the priesthood, and accept celibacy more or less willingly as part of the bargain.
A celibate priesthood creates problems; so does a married priesthood. The trials of ministers’ families are well known in the United States. Can you imagine what it would be like to be a priest and have several rebellious teenagers to supervise? Paul said that a bishop should be a man who can govern his own household well; Paul was celibate.
There is also the difficulty in combining a married and celibate priesthood in the same church. My understanding is that in the Orthodox churches celibates who are not monks are not assigned to parish duties. They live in the bishop’s household so that they have a community to support them.