Should women become pastors?
The Bible draws a connection between the home and the church. Just as there is a role distinction at home—where the husband is called to lead the family—there is also one at church.
At home men are proving their fitness to be elders (pastors), and at church they are the ones who are given that role. Paul says explicitly, "I do not permit a woman to teach or to exercise authority over a man" (1 Timothy 2:12). And those two functions—teaching and exercising authority—are the functions of the elder.
It's not a problem for a woman to minister in hundreds of ways in the church, but the office of leadership and teaching of men is preserved for spiritual and godly men.
Why didn't Jesus choose women as some of his apostles?
The Twelve are all men. That was intentional, because they are all given incredible authority to found the church. They are like pastors, only they have more authority than pastors.
But Jesus did call women, and he called them into significant ministry. Read the beginning of Luke 8 or see the role of women at the Resurrection. Jesus broke significant taboos in the way that he elevated the role of women. It was counter-cultural to have Mary sitting at his feet learning like a rabbinic student at the feet of his teacher. And it was counter-cultural for him to have women so closely attending him, providing for his needs, and for him to be so merciful to the women of the street.
Jesus was pro-woman to the max. But he did not choose women to be apostles. That wasn't because he was enslaved to his times. It was because, in coherence with the rest of the Bible (Genesis 1-2, Ephesians 5, 1 Corinthians 11, and 1 Timothy 2), he believed that it would be healthy for the church and the family if men assumed the role of Christ-like, humble, caring, servant-leaders, and if the women came in alongside with their respective gifts to help carry his leadership through according to those gifts.
So I sympathize with any confusion on this matter, and I pray that the Lord would give you light to see that it's really not very complicated: God has ordained that in the home and in the church men assume a special role of responsible leadership and teaching.