I remember reading a webpage about the issue of calling someone father. One of the points made against the practice was an Old Testament passage of someone asking another person to be his father spiritually.
I don't know exactly what you are referring to, but lets look at some of the usage of
Father in the Old Testament. The most interesting usage is probably the way in which God identifies himself as a Father to his people. The adjective "spiritual" isn't even introduced, he just pronounces that he is the father of Israel and likes the various things that he does and feels to those that a Father does and feels.
The word use used several hundred times so this won't cover them all, just a few to show this pattern.
To start with, there is an interesting reference where the Lord is speaking to David and promises to give him a son, but also that that son will be His son and that He will look after him as a Father:
Behold, a son shall be born to you [...] and I will give peace and quiet to Israel in his days. [...] He shall be my son, and I will be his father, and I will establish his royal throne in Israel forever. -- 1 Chronicles 22:9-10 (ESV)
This usage is very parallel to the language you find in many of the prophets (Jeremiah, Isaiah, etc.) where God is comforting his people by claiming them as his own. Two examples of many:
So shall you be my people, and I will be your God. -- Jeremiah 11:4 (ESV)
With weeping they shall come, and with pleas for mercy I will lead them back, I will make them walk by brooks of water, in a straight path in which they shall not stumble, for I am a father to Israel, and Ephraim is my firstborn. -- Jeremiah 31:9 (ESV)
The Psalmist also shows helps draw this parallel:
As a father shows compassion to his children, so the LORD shows compassion to those who fear him. -- Psalm 103:13 (ESV)
And also by Solomon:
[...] the LORD reproves him whom he loves, as a father the son in whom he delights -- Proverbs 3:12 (ESV)
This identification is also not just one way, Isaiah shows that he indeed understands God to play this role:
For you are our Father, though Abraham does not know us, and Israel does not acknowledge us; you, O LORD, are our Father, our Redeemer from of old is your name. -- Isaiah 63:16 (ESV)
The prophet Malachi also laments the fact that although God is the Father of his people, he is not properly regarded as such.
"A son honors his father, and a servant his master. If then I am a father, where is my honor? And if I am a master, where is my fear? says the LORD of hosts to you, O priests, who despise my name. [...]"-- Malachi 1:6 (ESV)
Have we not all one Father? Has not one God created us? Why then are we faithless to one another, profaning the covenant of our fathers? -- Malachi 2:10 (ESV)
Judges 17:10 And Micah said unto him, Dwell with me, and be unto me a father and a priest, and I will give thee ten [shekels] of silver by the year, and a suit of apparel, and thy victuals. So the Levite went in.
Judges 18:19 And they said unto him, Hold thy peace, lay thine hand upon thy mouth, and go with us, and be to us a father and a priest: [is it] better for thee to be a priest unto the house of one man, or that thou be a priest unto a tribe and a family in Israel?
As Wikis noted, Matthew 23 is the passage to which the person was probably referring:
“The scribes and the Pharisees sit on Moses' seat, 3 so do and observe whatever they tell you, but not the works they do. For they preach, but do not practice. 4 They tie up heavy burdens, hard to bear, and lay them on people's shoulders, but they themselves are not willing to move them with their finger. 5 They do all their deeds to be seen by others. For they make their phylacteries broad and their fringes long, 6 and they love the place of honor at feasts and the best seats in the synagogues 7 and greetings in the marketplaces and being called rabbi by others. 8 But you are not to be called rabbi, for you have one teacher, and you are all brothers. 9 And call no man your father on earth, for you have one Father, who is in heaven. 10 Neither be called instructors, for you have one instructor, the Christ. 11 The greatest among you shall be your servant. 12 Whoever exalts himself will be humbled, and whoever humbles himself will be exalted. Matthew 23:2-12 ESV
The idea is that men should not be exalted over us in such roles. The religious rabbis and teachers of the law were the most corrupt and dishonorable to God. Jesus commands us to not seek such titles for ourselves, nor give them to others, but to exalt God as Father and Teacher and Master.