Jesus said in the Bible "Do not call anyone on earth your father; for One is your Father, He who is in heaven.” (Mat 23:9 NAB). Why do Catholics call their pastors “Father” then?
First, let’s figure out if Jesus was being literal or figurative when he said this. Do you call your male parent “Father”, “Dad”, or any other name that implies paternal headship? If you do, you’re going against what Jesus said; if he’s speaking literally. So I don’t think anyone who makes this accusation really believes that he was being literal. Beyond that, Jesus himself says “Father Abraham” twice in Lk 16:24 and 30. Paul says he has become our father through the gospel in 1 Cor 4:15. Paul refers to "Father Issac" in Romans 9:10. So either none of these guys realized Jesus was being literal (including Jesus) or he was speaking figuratively.
An interesting thing in the Bible is a little thing called context. What was the context that Jesus said this in? Jesus was chewing out the Pharases for being proud and seeking honor for themselves at every opportunity. The Father comment was one of a string of visible signs of the Pharases' authority. He also said call no one “teacher”, why doesn’t anyone bring this up to our school system? Jesus was saying that no one can glorify themselves for being a teacher, for all wisdom comes from God. No one can glorify themselves for being a father for all creation was created by God.
The real question is why do Catholics still use the term Father? Why not pick another word (like Reverend) and avoid the issue all together?
The New Testament is full of the Apostles referring to themselves as Father and the people they're mentoring as "Child" or "Son" (Paul calls Timothy Son and Child many times and says I am your father through the gospel as noted above; Peter and John do the same thing). Catholics just kept the tradition up from that time. We believe that ordained men continue in Apostolic Succession; so they fill the role in the Church today that Apostles did after Jesus' death. That's why we give them the same titles as the Apostles.
In addition, it’s the most fitting word to describe a priest’s relationship with the laity (those who aren’t ordained). Priests, in persona Christi, provide us with our food (Eucharist), with forgiveness (Reconciliation), they lead and teach us (homilies), they provide for our families (through giving their lives in service), they give advice (through spiritual direction), and do many other fatherly things. What better word can there be to describe what our priests do for us? Maybe “Rock Star”, but that’d be a bit much.
As a parting shot, Protestants call their leaders names too; Pastor, Reverend, and Minister for example. What's the difference? It's still a title that sets that person apart as a spiritual leader and that's the heart of what Jesus was condemning. So use the titles as they’re given, but remember that all earthly fathers only derive their position from our heavenly father. Without him as their father, our spiritual leaders are powerless.