The idea that men aren't "sensitive" is bullshit. They just don't express it like women, nor should they be expected to. It's related to brain structure, it seems, and hormones. Testosterone isn't exactly "the chat hormone."
In addition to the above, I suspect it is also related to evolutionary development. "Take it like a man" is not an accidental formulation, but rather an ingrained evolutionary one. When sunset is close; when you don't want to be trapped overnight away from the village and exposed to predators; when you are tired, beat up, wet, cold, and maybe injured: now is not the time to emote and to discuss your feelings. Now is the time to "take it like a man", and to get yourself and your compatriots back to the village. The emoters and discussers died off ages ago. Our fathers took it like men.