1 Tim 2 :

^{Instruction 11} A woman should learn in quietness and full submission. ¹² I do not permit a woman to teach or to assume authority over a man; she must be quiet. 

^{Reason 13} For Adam was formed first, then Eve. ¹⁴ And Adam was not the one deceived; it was the woman who was deceived and became a sinner. 

1. The serpent chose first of all to temp EVE and not Adam.  Secondly, it chose at a time when she was not with Adam.
2. After EVE had eaten the fruit from the tree of ‘knowledge of good and evil’, her eyes were opened – knowing “good and evil’ . Then with that knowledge she brought the fruit and gave it to Adam.

James 1:  ¹⁴ but each person is tempted when they are dragged away by their own evil desire and enticed. ¹⁵ Then, after desire has conceived, it gives birth to sin; and sin, when it is full-grown, gives birth to death. 

3. Adam took and ate the fruit from Eve not because he was deceived. We can speculate various scenarios why Adam took and ate, but “deception” was not one of them. 

4. Each individual is responsible for their own sinful actions.  THERE IS NO EXCUSE.

Context:

^{2 Tim 2:16} Avoid godless chatter, because those who indulge in it will become more and more ungodly. ¹⁷ Their teaching will spread like gangrene. Among them are Hymenaeus and Philetus,

^{1 Tim 3:3} As I urged you when I went into Macedonia, stay there in Ephesus so that you may command certain people not to teach false doctrines any longer.

^{1 Tim 4 :11} Command and teach these things. ¹² Don’t let anyone look down on you because you are young, but set an example for the believers in speech, in conduct, in love, in faith and in purity.

To have authority – on doctrine or laying the foundation of faith before the Scripture was completed. In today’s application ( post canonization era ), Not only women but men or anyone else should not misinterpret the Scripture “which one considered right according to his own eyes”

James 3: 1 Not many of you should become teachers, my fellow believers, because you know that we who teach will be judged more strictly. 

Not only women are not allowed to teach ( with doctrinal authority ) but not all men should teach either.

Paul’s instructions to Timothy goes on and touched many other areas of Church’s lives and practices. “Women should not have authority ( on matter of doctrine ) over men” is only a small part. We just can not tear out that small part and interpret it as “passe”

What other Scripture says:

Mandate to all believers:  

Matt 28: ¹⁸ Then Jesus came to them and said, “All authority in heaven and on earth has been given to me. ¹⁹ Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, ²⁰ and teaching them to obey everything I have commanded you. And surely I am with you always, to the very end of the age.”

Can women then be a pastor or teaching elder ?

This would fall under the qualification of an elder / pastor.