I don't think it has anything to do with what women are capable of mentally, but rather what the players and would-be women managers would be capable of emotionally. Women are certainly capable of doing the job, but there is a lot to managing we don't see and can't comment on. I think the interpersonal nature of the job would be difficult for a woman not only because of the uphill battle to gain respect, but because she'll be in the clubhouse and locker rooms, and have to mentor and berate. She might be built to handle all of that, but it's not just about her; it's about the 25 players on the roster, the rest of the coaches, the GM and management...there are a lot of hurdles to jump over.
If anyone says, however, that women "just aren't capable" of it, my mind automatically thinks about all those comments about black players "just not being capable" to play in MLB or "not having what it takes" to be managers or in the FO.
That said, I would most certainly advocate a woman as a GM, rather than as a team manager. Women's mettle isn't what I question; what I question is men's ability to accept talent over perception.