I take it as a natural reaction to overload of stress/emotion/pain. Being able to cry is physiologically beneficial (you get rid of cortisol) and psychologically it can help you process the things you're going through more quickly. Trying to appear though by not crying seems counterproductive to me, but I understand in some cultures it is not socially acceptable to cry, especially for men.

To me, if you're crying you're admitting that something is stronger than you, that you're powerless, and i still find it useless, i guess that i just have a bad image of it(, it can be beautiful though, like tears of joy, or of an emotion which isn't defeat). But i clearly(, and subconsciously,) don't treat men, women, or children, in the same point of view in regard to crying, i'd never think of saying "man up" to a woman hurt to the point of tears, yet i find it admirable when a man swallow his pain, and straighten his profile in order to act after whatever happened, that's the common thinking, i'm not the weird one here(, even if my descriptions are very imperfect), but since modernity changed so many things they may end up suppressing the differences between men and women, or not, w/e.

If I suppressed my emotions, I would still be influenced by them, but I would have no conscious control over them, which would again result in limiting my rationality

On the contrary, suppressing your emotions helps to act rationally without being overwhelmed by them, and i.m.o. there's no real difference between emotions and reason, since our feelings can be explained rationally, we're often saying that "reason ignore the heart's own reasons", but that's not true, we are indeed influenced by subconscious feelings that we would be unable to analyse, but that's a minor side and i don't make a distinction between the cold reasoning and the hot emotions, i'm deciding with both a'd i think almost everyone does the same.

I find the terms inner strength and beauty to be also very vague.

100%, i realized it when i was writing the examples, and the example you gave me is another very good one, you can indeed find effeminate/weak persons who are "tough motherf*ckers", i didn't give enough thought behind what "internally strong" may mean, and it also depends on the situation, it's not because you're weak or ugly internally at one time of the time that you can't act beautifully or strongly at another time.

I agree with you that it's reductive to stop on two adjectives.

Well, it doesn't come from me and i have a story and some good memories from it. But in a few words, i asked someone special(, ~9 years ago,) if he had a motto, and he told me that the masonic triangle is "Strength · Beauty · Wisdom", i still haven't checked if it's true(, but discovered a few years later that it's in the Kabbalah). It stayed in my mind and i naturally decided to apply it to men and women and divide it in internally//externally. Just to say that somewhere.
While reductive, i think it has a lot of truth in it.

I don't see any reason to propagate just one way for men and one way for women.

Men have testosterone, have sexual fantasy when they touch women, and read comics when they imagine themselves fighting.
Women have estrogens, in their fantasy they imagine themselves being touched, and read romantic novels when they're preparing themselves for the unavoidable desire they'll attract.

Yeah, i'll need to edit this message, if you're reading this line give me 30-40mn i want to do something first.