I have to say that I never much thought about what a man is which leads me to speculate about the motivation behind the question. Perhaps the pursuit of such an answer implies a certain insecurity regarding how one measures up to some cultural norm the attainment of which transfers to one the hope one has developed past some insecurity. And since humanity is upside down to reality, one would likely expect that any definitions of manhood that are popular would in fact be a state of mental illness. A man, for example is a cowboy who silently suffers, who conceals his pain and rides on into the sunset and the whole emotionally cut off notion embodied in the word macho, and certainly not the kind of advise that some source of real knowledge like the Bible might suggest, that except as a little child you will not enter the kingdom of heaven.
So if I had to ask myself what it is to be a man, I hear these world in my head that I heard somewhere, I consider him a man only, who can honor the wolf and the sheep entrusted in his keeping. That to my mind implies a reference to the holy trinity, the trine principle at the core of existence, the holy affirming, the holy denying, and the holy reconciling, as suggested in alchemical transformation.
The principle, I think, is represented in the story of the man on a journey with a cargo of a wolf a sheep and a cabbage, who has to cross a river that has no bridge, and who can carry only one of the three at a time.