I like this question.
Mt 23:9: “CALL NO ONE ON EARTH YOUR FATHER; you have but one Father in heaven.” – a literalistic interpretation means no person on earth could be called father. Therefore we could not call our dads, father either. But if we are to take a literalistic approach then how come we find in the gospels and other books of the NT, which were written after the Resurrection, the authors using the term ‘father’ to describe both natural fathers and spiritual fathers?
Do you believe that scripture does not contradict itself? If you are a Christian who believes the bible is the inspired Word of God then you must believe that scripture maintains integrity across itself, that one part of scripture does not contradict another. In this way, we have to consider other scripture on the matter rather than just one or two verses.
Catholics believe and affirm what Jesus said in Mt 23:9. If we read the scripture in context we see Jesus using this term ‘father’ in conjunction with the Pharisees and scribes. The scribes and Pharisees were usurping the role of God the Father. Also, many Roman leaders were in those days calling themselves ‘Father’ and commanding people to burn incense to them in worship. Jesus is using hyperbole to make the point that no one should take the place of God the Father since you only “have but one Father in heaven”. This is similar to where Jesus uses hyperbole in Mt 5:29 where he says to gouge your eye out if it causes you to sin. If Christians were to interpret that literally we would all be amputees.
Scripture does not contradict itself. Here are a few other scriptures that make a case against a literal interpretation:
Jesus uses the term ‘father’ often in the gospels
Mt 10:35 (NAB): "For I have come to set a man against his father, a daughter against his mother, and a daughter-in-law against her mother-in-law."
Luke 16:24-30: Jesus calls Abraham, ‘father Abraham’ in the parable of Lazarus
Angel Gabriel about John the Baptist
Luke 1:17 (NAB): “He will go before him in the spirit and power of Elijah to turn the hearts of fathers toward children…”
Angel Gabriel about Jesus
Luke 1:32 (NAB): "He will be great and will be called Son of the Most High, and the Lord God will give him the throne of David his father.
Mary calls Abraham her father
Luke 1:55 (NAB): "…according to his promise to our fathers, to Abraham and to his descendants forever."
Luke 1:72 (NAB): “to show mercy to our fathers and to be mindful of his holy covenant”.
Luke 1:73 (NAB): “and the oath he swore to Abraham our father, and to grant us that,”
Mary calls Joseph father of Jesus
Luke 2:48 (NAB): “…Your father and I have been looking for you [Jesus] with great anxiety.”
The new Jewish Christians call David their father
Acts 4:25: “you said by the holy Spirit through the mouth of our father David, your servant: ‘Why did the Gentiles rage and the peoples entertain folly?”
St. Stephen addresses the ‘fathers’ in the crowd-
Acts 7:2: “And he replied, “My brothers and fathers, listen. The god of glory appeared to our father Abraham…”
Acts 7:32: “I am the God of your fathers…”
St. Paul addresses the ‘fathers’ in the crowd:
Acts 22:1: “My brothers and fathers, listen to what I am about to say to you in my defense.”
Romans 4:11 – Abraham a spiritual father, not just a natural father
“Thus he [Abraham] was to be the father of all the uncircumcised…”
Romans 4:16: “follow the faith of Abraham, who is the father of all of us.”
James 2:21: “Was not Abraham our father justified by works when he offered his son Isaac upon the altar?”
Paul, a spiritual father:
1 Cor 4:15: “Even if you should have countless guides to Christ, yet you do not have many fathers, for I became your father in Christ Jesus through the gospel.”
1 Tim 5:1: “Do not rebuke an older man, but appeal to him as a father.”
Phil 1:10: “I urge you on behalf of my child Onesimus, whose father I have become in my imprisonment.”
John writes to elders in the church calling them fathers and exhorting them to teach their sons:
1 Jn 2:13–– “I am writing to you, fathers, because you know him who is from the beginning.”
John writes to more than just physical fathers but to spiritual fathers who know him who is from the beginning.
All fatherhood is derived from the Father:
Eph 3:14-15 – “For this reason I kneel before the Father, from whom every family(1) in heaven and on earth derives its name.”
(1) The Greek for family (patria) is derived from the Greek for father (pater).
See also "Blessed to be Catholic"