That's good it worked out for you. Many women tell their man it's OK to cry and be vulnerable, then are completely disgusted and sometimes leave them when it happens.
Either way, it works out.
Look from their perspective.
"My man is so smart, competent and emotionally stable. I can rely on him for anything!"
"Oh no he's crying, does this mean our family won't survive? What do I do?"
It's not anything more complicated than that. Women can probably chime in to tell me if I'm right or wrong, but this is a human perspective, because children will feel the same way if the father cries.
Crying is an expression of bottled up emotions, not an acceptance of defeat. Someone can cry and be invigorated to try harder to deal with their problems or they can cry but still be supportive to their spouse and provide emotional stability.
Womens' reactions are dependent upon their personality, their values, their view of the other person, the environment, their current emotional state, their biology and a lot of other factors at any given moment. This explains the fact that some people in this thread talk about how their crying led to more fulfilling relationships why others talk about break ups and loss of trust.
Even the point about children is completely arbitrary. Will children feel that their family won't survive due to their father crying about a lost relative? Doesn't it depend on their age? Furthermore, children need to see that their parents are humans and how to express their emotions. The alternative is that they find more indirect ways to do that like alcoholism, abuse, self-harm, extreme escapism and many other banes of today's society.
You covered some reason for it on the woman’s part. While he (OP) seemed to only be talking about the man’s reason (motivation) to not act like that.