Biblical support is tricky, since there’s not much about anyone being a preacher/pastor. Those aren’t the usual terms in the New Testament for church leadership. When it comes to speaking, there’s more about proclaiming, prophesying and teaching, and for all of those we have both examples and instruction that includes women. Women proclaimed the gospel message of Jesus’ resurrection (to men!), women prophets demonstrated the inclusive work of the Holy Spirit, a woman (with her husband getting second billing) taught Apollos what was missing in his understanding of the gospel.
I think Paul’s major letters are clearest about how we are all to use our gifts – including leadership and speaking gifts – in the church:
For as in one body we have many members, and not all the members have the same function, so we, who are many, are one body in Christ, and individually we are members one of another. We have gifts that differ according to the grace given to us: prophecy, in proportion to faith; ministry, in ministering; the teacher, in teaching; the exhorter, in exhortation; the giver, in generosity; the leader, in diligence; the compassionate, in cheerfulness. (Romans 12:4–8)
The difference comes from the grace – not the gender – given to us. This becomes abundantly clear a few chapters later when Paul greets the church leaders in Rome and coming to Rome, nearly half of whom are women (Romans 16).
To Corinth, which apparently had some issues with the poor and the women being excluded from full church participation, Paul goes on for chapters about this. He speaks of how both men and women can prophesy and both rich and poor can partake of the Lord’s supper together (chap. 11). He emphasizes that the Spirit gives gifts to all without looking at worldly distinctions (chap. 12). While he doesn’t rank people, he doesn’t shrink from ranking the roles:
And God has appointed in the church first apostles, second prophets, third teachers; then deeds of power, then gifts of healing, forms of assistance, forms of leadership, various kinds of tongues. Are all apostles? Are all prophets? Are all teachers? Do all work miracles? Do all possess gifts of healing? Do all speak in tongues? Do all interpret? But strive for the greater gifts. (1 Corinthians 12:28–31)
This passage is clearly addressed to the whole church, men and women. They are all encouraged to strive for the greater gifts of apostleship, prophesy, teaching, etc. The famous love chapter explains how these gifts are to be used, not to puff up the one but to serve the many. Then chapter 14 gives the clearest New Testament picture of what church services should look like:
Pursue love and strive for the spiritual gifts, and especially that you may prophesy. … Now I would like all of you to speak in tongues, but even more to prophesy. … When you come together, each one has a hymn, a lesson, a revelation, a tongue, or an interpretation. Let all things be done for building up. … For you can all prophesy one by one, so that all may learn and all be encouraged. … So, my friends, be eager to prophesy, and do not forbid speaking in tongues; but all things should be done decently and in order. (1 Corinthians 14:1, 5, 26, 31, 39)
Of course, this chapter also has two verses that tend to get extracted to teach the opposite message. Verses 34–35 say three times that women are not to speak in church. When these verses are put in context, and when one remembers that this half of the letter is where Paul has turned to address “the matters about which you [the Corinthians] wrote” (1 Corinthians 7:1), it seems fairly clear that the jarring words contradicting Paul’s message are in fact the Corinthians’ words that he is quoting and rebuking. That’s why they’re surrounded by Paul saying otherwise. They thought the women should shut up and learn at home from their husbands; Paul teaches that everyone can speak in an orderly, intelligible way so that everyone learns at the service.
Paul’s whole message to the Corinthians in chapters 11–14 is about inclusive participation in church. It’s a shame that a couple verses that likely present the toxic position that compelled him to pen these amazing chapters have been used to dilute his message as if it didn’t actually apply to women.