This question of whether one's sex male or female mattered to Paul is perhaps easier understood if we start the investigation with another of Paul's comments to Timothy.
When I call to remembrance the unfeigned faith that is in thee, which dwelt first in thy grandmother Lois, and thy mother Eunice; and I am persuaded that in thee also.
2 Tim 1:5
But continue thou [Timothy] in the things which thou hast learned and hast been assured of, knowing of whom thou hast learned them; And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus.
2 Tim. 3:14-15
In these passages, we find Paul praising the two women teachers Lois and Eunice. He exhorts Timothy to continue in the things taught him.
With that in mind, when we read the so-called admonition against women teachers, we should question what Paul is actually telling the readers.
But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.
1 Tim. 2:12
Is Paul contradicting himself between the writing of 1 Tim and 2 Tim or is there something deeper here? In one place he supposedly tells women not to teach and then in another praises the two women teachers!
The word "authority" from the 1 Tim 2:12 and the word "scriptures" in 2 Tim 3:14-15 will guide us. In other words, what is the authority? The sex of the teacher or something else?
from autos, "self," and a lost noun hentes, probably signifying working (Eng., "authentic"), "to execise authority on one's own account, to domineer over," is used in 1Ti 2:12, AV, "to usurp authority," RV, "to have dominion." In the earlier usage of the word it signified one who with his own hand killed either others or himself. Later it came to denote one who acts on his own "authority;" hence, "to exercise authority, dominion."
Vines Expository Dictionary of New Testament Words
Paul is not correcting the sex of the teacher, but rather, the source of authority; that is, self or scripture.
Who came before Eve? Who came before Adam?
Knowing this first, that no prophecy of the scripture is of any private interpretation. For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost.
Again, Paul is not arguing about Lois or Eunice or any other female teacher. In Paul's time, the finality of God's word via scripture was being fulfilled. In his time, it was the apostles (men) that had the authority. Subsequently, it is scripture that has the authority. If a woman rightly divides the words of God and if a man wrongly teaches scripture, Paul is not saying pay attention to the sex of the teacher. Paul is saying know from whom (scripture) you have learned.