I don’t think they are necessarily saying it’s the other way around for women. I think in the case of a man’s word, I think it harkens back to when women had no power, couldn’t own property, couldn’t make business deals, so men were addressed as the one giving their word. I think just like man and men can mean all people, this old saying about a man’s word can easily be changed to a person’s word. Are you a man or not? Well, yes, it is more acceptable for women to cry, but it’s more situational than anything. A woman at work can’t cry just like a man in many situations or it looks bad. Men can cry when it comes to emotional sadness or happiness regarding family and tragic events, and it’s fine. No one is going to look down on a man who tears up when seeing his child accomplish something great, or cry when he loses his wife to a tragedy. Men traditionally had the responsibility of showing physical strength, and ability to earn a living, and were in roles that have an expectation of acting “like a man.” Of course, this is all changing in modern day. The doors are more mixed up now.