St. Paul, speaking in the Spirit, and recorded in Holy Scripture for posterity, uses the term father in reference to men on earth, specifically to preachers in relation to their parishioners.
1 Corinthians 4:15 For though you have countless guides in Christ, you do not have many fathers. For I became your father in Christ Jesus through the gospel.
Philemon 1:10 I appeal to you for my child, Onesimus, whose father I became in my imprisonment.
Philippians 2:22 But you know Timothy's proven worth, how as a son with a father he has served with me in the gospel.
1 Thessalonians 2:11-12 For you know how, like a father with his children, 12 we exhorted each one of you and encouraged you and charged you to walk in a manner worthy of God, who calls you into his own kingdom and glory.
1 Timothy 5:1-2 Do not rebuke an older man but encourage him as you would a father. Treat younger men like brothers, 2 older women like mothers, younger women like sisters, in all purity.
Let's examine what Jesus says.
Matthew 23:9-10
And call no man your father on earth, for you have one Father, who is in heaven. Neither be called instructors, for you have one instructor, the Christ.
First of all, if you aren't going to call your pastor Father, then you had better not call anyone in the congregation 'instructor' or 'teacher' either.
But more to the point, it's clear Jesus is making an absolute statement: call no one your father on earth, for you have one Father, who is in heaven. The statement is either literal and means "call no human being on earth by the term father" or it is in some sense figurative, with the figure in the word "call," that is, "realize that no man on earth is really your father, even though you have many fathers on earth, for there is only One True Father."
Well, if it's the former then how is it that we all call our fathers father? How does one justify that in light of Jesus' statement? "Call no man father" does not make room for biological exceptions. That is, if there is a figure here it certainly can't be in the negative particle because the whole force of the statement is most obviously aimed at earthly, biological fathers. There is no way the statement means "Call your dad father but nobody else."
So the figure is obviously in the word "call:" realize that some words we use towards men are used only in shadowy ways because they belong to God. To "call" something by name in the Bible has great importance. Think of all those name changes in the Bible: God calls a thing what it is. To name something is supposed to directly speak of its essence. But when we call our earthly fathers father we just can't be using words that way. Our fathers are shadows, reflections, images (often poor ones) of the ultimate reality. We could just as well say that no wife should call her husband husband because there is only One Husband who is in heaven, Christ the Lord. Or, no one ought to call the lords in the House of Lords lords because there is only One Lord. In every case we are not thereby calling for some silly undoing of plain speech but for a realization that God is the reality and things down here are the shadow.
Source:
Gottesdienst Online: Call no man father...the definitive post