I do meet with women, regularly, just never alone. My refusal to meet alone with women is hardly irrational. It is one of the safest and sanest choices a man can make in the current environment where a mere accusation is often enough to cause the loss of a job and future prospects.
I sincerely hope it never happens to you, but odds are high that it will if you acquire enough power at work. Not a popular view, I know, but still true.
Contrary to popular belief and widespread practice, 1:1s are not essential to developing employees. There are lots of other very effective ways to develop people on a team. (That's right, the men on my teams didn't get 1:1s either. And yet, somehow we got stuff done.)
This is exactly why I don't manage anyone any more. It's so tiresome when people with ten or twenty or thirty years less experience fight you every step of the way. I made enough doing that, now I make enough doing something else.
I've been on the pointy end of a false accusation by a woman in my team who was upset I insisted on supervising and double checking her work (which was extremely poor). Lucky me, the accusation wasn't sexual and double lucky she was a terrible liar. But if you think false accusations are rare you are pretty naive and probably just were never in a position to make an enemy of a woman.
If the accusation you were at the other end of "wasn't sexual", I'm not sure what it has to do with this story, this thread, or with the gender of the accuser. I've been falsely accused of things at work by dudes, too. That is a thing that does happen.
https://www.theregister.co.uk/2015/11/06/linus_torvalds_targ...