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Thank you for your question, it’s an interesting one that I have thought of before. There are a couple primary reasons for why there are no women authors in the Bible:
The entire Bible, all of God’s Word, is “breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness,” (2 Tim. 3:16). In his “first” letter to Timothy, Paul writes, “I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet” (1 Tim. 2). The primary purpose of having God’s Word written is to be able to continue teaching it to the future generations of Christians. It is primarily used for teaching (first from the Holy Spirit - 1 Cor. 2:6-16, then from gifted men - Rom. 12:3-8), which is a role Paul makes clear is not for women (when men would be sitting under their teaching). In all of Paul’s letters he is very clearly teaching doctrine to the various churches and disciples he is writing to. Since these written books were used for teaching, it would go against God’s Word to have female authorship.
Does this mean that women are unable to understand God’s Word, unable to teach entirely, unable to be wise? Absolutely not. Women should be good stewards of God’s Word, should teach other women and children about the Lord and how we must respond to His grace, and grow in wisdom! I know I certainly desire to marry a wise woman and have the mother of my children be wise and teach them true doctrine from God’s Word when I am not there to do so.
There were almost no women who were educated during the times that Scripture was written (and for most of history after). Of course, this does not mean that women were or are less intelligent, but they were very rarely educated in ways of reading and writing.
Women play a crucial role in this world and God uses women to further His kingdom in tremendous ways. However, I do believe that since it is not the woman’s role to teach or exercise authority over men then that involves writing the very Scriptures that are used to teach.