Unfortunately this point is not clearly understood for the majority of the Christian World because there is little written on the subject of the priesthood. It is hard to know exactly what Paul was referring to in this passage without some further light and knowledge shed on this subject.
From the King James Version of the Bible, the only suggestions given to Titus for the selection of worthy men to become Elders are found from Titus 1:5-6:
"For this cause left I thee in Crete, that thou shouldest set in order the things that are wanting, and ordain elders in every city, as I had appointed thee:
If any be blameless, the husband of one wife, having faithful children not accused of riot or unruly."
But Paul also taught Timothy about the Priesthood,
"And no man taketh this honour unto himself, but he that is called of God, as was Aaron.
So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee.
As he saith also in another place, Thou art a priest for ever after the order of Melchisedec." (Hebrews 5:4-6)
This means that in order to become a Deacon, Teacher, Priest, Elder, Seventy, Pastor, Apostle, Prophet or any other authority, that man must be called of God as was Aaron (through the prophet having authority, Moses in this case) or as Melchizedek (God speaks to him directly). In the case of Titus, he had had authority given to him by Paul, who had received his authority from his call by Jesus Christ and by the Presiding authority, Peter, who held the keys to call people to the offices of the Priesthood and to direct the affairs of the Church under the direction of Jesus Christ. Titus was given authority to set up the church in Crete and to call Elders and Bishops to watch over the church.
If God wanted to call an man to be an Elder who did not have children at all, he could very well do so. He called the prophet Samuel to be a prophet when he was a small boy and used Joseph the son of Jacob as a prophet before he was married.
In the case that a man does have children, if they are well behaved, he may effectively be able to watch over the affairs of the church as well as those of his own family. A man's primary responsibility is to his family and if his children are causing riots and are unruly, he cannot effectively focus on the needs of the church and properly fulfill his responsibilities as a father simultaneously.
God speaks to men today and calls them by his appointed servants.
"Surely the Lord God will do nothing, but he revealeth his secret unto his servants the prophets." (Amos 3:7)