All Christians are priests — "a royal priesthood, a holy nation" (1 Pet. 2:9).
It is true that all Christians share in the priesthood of Christ through Baptism, but this common priesthood is different from the ministerial priesthood. First Peter is referring back to what was said of Israel in Exodus 19:6, "You shall be to me a kingdom of priests and a holy nation." Within the priestly nation of Israel, however, existed a distinct ministerial priesthood, the priesthood of Aaron. It’s the same for God’s people in the New Covenant.
When will the Church get out of the Dark Ages and start allowing women to be priests?
This is not a case of discrimination against women. Of all the Saints the Catholic Church reveres, she reveres a woman, the Virgin Mary, far and above the rest. And there are many women who are leaders in the Church. Most parish religious education programs, for instance, are run by women directors. But a priest is more than merely a leader, he is a father. Paul said, "I became your father in Christ Jesus through the gospel" (1 Cor. 4:15). In essence the priesthood is spiritual fatherhood. And while a woman is free to be virtually whatever she wants to be, the one thing she cannot be is a father.
Why do Catholics call priests "Father" when Jesus said, "Call no man your father upon the earth: for one is your Father, which is in heaven" (Matt. 23:9).
What, then, do you call your mother’s husband? … Obviously, Jesus did not mean for us to take this saying literally. Rather He was speaking in an exaggerated way to make the point that all life and wisdom come to us, not from human beings, but from God. In fact, the tradition of calling priests "Father" is biblical. Judges 18:19 says, "Come with us, and be to us a father and a priest." And in First Corinthians 4:15, Paul says, "Though you have countless guides in Christ, you do not have many fathers. For I became your father in Christ Jesus through the gospel.”
Read more about the priesthood in the Catechism of the Catholic Church.
Why does the Catholic Church say priests must be celibate when the Bible says bishops should be "the husband of one wife" (1 Tim. 3:2) and Peter himself was married?
Jesus (who was celibate) said there will be "eunuchs who have made themselves eunuchs for the sake of the kingdom of heaven. He who is able to receive this, let him receive it" (Matt. 19:12). Celibacy is not a doctrine of the Church, but merely a discipline; and disciplines can and do change over time. Obviously, it would not have been possible for the early Christians to make celibacy mandatory, as Christianity was a new faith made up of converts, most of whom were already married. Though not mandatory, however, celibacy was preferred for ministers. Paul, like Jesus, was celibate; and he wrote, "I wish that all were as I myself am. ... He who marries ... does well; and he who refrains from marriage will do better" (1 Cor. 7:7, 38). And even though married men were permitted to serve as priests in the early centuries, unmarried men, once ordained, were forbidden to marry.