That's one of the weaker attempts at shaming someone into doing something foolish and unnecessary that I've encountered.

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.

Obviously you are not up to date with the current state of militant feminism in many parts of the western world. Some women will easily make up accusations for personal reasons and even for career advancement. Not meeting them one-on-one in a professional setting is a perfectly valid protection from this. (Why would you need to meet them one-on-one in a workplace anyway? Do you have secret projects you don't want other co-workers to know about?) (Not all women do this obviusly, but a small part. Just like not all men harass others. But it takes one to destroy a career.)

No, it's getting quite common. The pence rule, they call it in America.

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.