Teaching in the church implies a certain level of self-direction and judgment, and a de facto air of authority. That is the context in which I echoed Paul, where having women teach is a foolish danger. Of course, this same reasoning, the weakness or vulnerability of women to deceit, has effects elsewhere and that is why the passage speaks beyond merely the church.
But it doesn't automatically apply in the same way everywhere. Because scripture specifically commends women teaching some audiences, on some subjects, under male authority and direction, we know that those are good. In these contexts, the deficiencies in the sex are managed and the virtues channeled.
The nature being the problem does not, in any way, imply a bar from all teaching in all contexts. It would, however, imply a need, a warrant, and a different or greater manner of direction/accountability when teaching, and limited subject matter. I think scripture gives us all of those. My position requires at least something of that sort, but it does nothing to require a total ban beyond that.
Titus 2 says nothing about the aged women teaching younger women "under male authority and direction."
Of course it does. It's built-in. Are you suggesting that believing women can somehow teach other women without being under the direction or authority of men? Who are these women who don't have husbands, fathers, or elders?