In Matthew 23:9, Christ is actually warning against looking to any man as a Father in the way God alone is our Father. Jesus was living in a time when religious leaders and even political leaders demanded divine worship (like the Caesars), and so our Lord was saying to His people: You don't do the same thing. Do not give to man that which is due to God alone.
As we see in the scriptures listed below, Christ did not literally mean that we cannot address others as "father", even in a religious context. Many who object to the Catholic custom of calling priests "father" forget that in Matthew 23 Jesus also says to call no man teacher, but they have no problem calling people teacher or doctor (which is the Latin word for 'teacher'). So the anti-Catholic is not consistent in his literalistic approach to Scripture.
Here are some scriptures showing that Matthew 23:9 was not meant to be taken literalistically:
1 Cor 4: 15 - "For if you have ten thousand instructors in Christ, yet not many fathers : For in Christ Jesus, by the gospel, I have become your father". This statement by St. Paul would contradict Christ if Christ had meant what He said in Matt 23:9 literally.
John 2:13 - "I write unto you; fathers, because you have known him (Jesus) who is from the beginning." John’s letter was addressed to churches in Asia Minor, and he seems to have no problem calling men in that church "father".
Acts 7:2 - "Ye men, brethren, and fathers, hear." Here, St. Stephen calls the Pharisees and council "fathers". Was he disobeying Christ?
Acts 7:38-39 - In these passages, as in many others in Acts, St. Stephen refers to the children of Israel who came before as "our fathers". (read all of Acts 7.)
Romans 4:1-16 - St. Paul refers to Abraham as "father" five (5) times.
Mark 11: 10 - "Blessed be the kingdom of our father David that cometh: Hosanna in the highest." Here, the crowds outside Jerusalem call David "father" as Jesus approaches.
Titus 1:4 - St. Paul does not refer directly to himself as "father" here, but he does make that connection by reminding Christians of his spiritual fatherhood that comes from God. He makes the same point in Philemon, where here identifies the Christian slave Onesimus, as being his son in the faith and he, Paul, as having become his father.
These are the writings and/or teachings of Saints Paul, Stephen, John and Mark. But what of the words of Christ?
Luke 16:24 - In Christ's parable of the rich man and Lazarus, (Luke 16:19-31), Jesus Himself uses the phrase "Father Abraham".
Matt 10:21-37, 15:4-6 - Jesus repeatedly refers to earthly men as "father" or "fathers".
If Jesus was being literal when He said "call none your father upon earth", then this would be a direct contradiction.
As Christians, we are spiritual brothers and sisters in Christ. And, just as St. Paul became the spiritual father of those early Christians in Corinth by preaching the Gospel to them (1 Cor 4:14-15) so our pastors, preaching the Gospel to us today and giving us new birth in Baptism are our spiritual fathers. We use the ward "father" as a sign of affection because St. Paul says, "Let the priests that rule well, be esteemed worthy of double honour: especially they who labor in the word and doctrine" (1 Tim 5:17).
