@Jim an Apostle you're attempting to logic around Paul's clear prohibition. That's not rightly dividing the word.
We're talking about teaching doctrine, not prophesying, not preaching the gospel. Those examples do not apply, but you had to use them because there are no examples of women teaching doctrine. Because none of the early churches allowed it, nor did they for close to 1900 years. Well ok, that's not strictly true (Rev 2:20); but you couldn't use that example either.
"Paul did not promote a ideology of Law but rather of Grace"
And yet he says "I do not allow a woman to teach". I am simply echoing what Paul said. I reject licentiousness. Using grace to cancel commands in scripture is kindergarden theology.
If you love Me, you will keep My commandments...He who has My commandments and keeps them is the one who loves Me; and he who loves Me will be loved by My Father, and I will love him and will disclose Myself to him
"Paul was not trying to establish a new Law"
Paul was an Apostle, as such he was forming churches and setting the standards for how they would operate; things which all the churches practiced.
So then, brethren, stand firm and hold to the traditions which you were taught, whether by word of mouth or by letter from us.
"Paul's instructions were not a one size fits all, for all time and eternity! Paul was speaking to a time and place."
This can be, and is, used to toss out any and all instructions in the NT and is a favorite of whose who would toss out scripture and 2000 years of theology to make them acceptable to modern ears. I reject it. Of course you had to go there, since Paul's prohibition is simple and straightforward; the only real way out of it is to start tossing out scripture, saying they don't apply to us today.
And this is really the crux of the matter. Prohibiting women from teaching is extremely offensive to modern ears, steeped in feminism and ideas of equality. Of course they don't want the old ways to apply to today.
You must choose....will you follow Christ and His ways or the ways of the world? It's one or the other, you don't get to have your cake and eat it too.