Little boys and girls have the same levels of a hormone (I forget its name) which enables crying. At the onset of puberty this hormone plummets to low levels in boys, but stays relatively high in girls.
Men have all the same emotions as women, but express them differently. Evolutionarily, for males to present themselves as vulnerable in a sexual and survival competition cannot have led to many females wanting a "weak" male to protect them whist they are pregnant (again). So holding onto emotions is bred into the gene pool.
I know women who always say "Jesus cried too" - this was in response to very real grief and loss. They want their men to express emotions on a woman's terms. These same women would scorn their man if he burst into tears and ran upstairs because he burnt the toast, or the gravy didn't come out right. (I have seen women do that - never men)
For me crying was something that only happened if my emotions had built to an explosive level. But then as a child I was often told
"What's up with you? If you start crying, I'll give you something to cry about!" A very common way of stopping boys becoming a "crybaby" at the time.
You are in such a terrible situation. My mother also has cancer. But I need to be supportive, not a gibbering wreck when I see her.
Personally, if I had cancer, I would need all my strength for my own fight - not to dissipate it on comforting others who are crying and needing my support to cope with their own feelings.
This is such a common issue for many men, that I cannot see that it is the fault of the WTBTS, except insofar as it perpetuates outmoded sex stereotypes.
You are being "strong" and supportive to those you love. The last thing a gravely ill person needs is to see a loved one crumple when they cannot give them what they need.
Crying is very cleansing for the soul, when the time comes you will have no problem. Just because somebody says you should be crying is no reason to feel bad about yourself if you don't.