You really don't need to reach that far. As a man if you are too often vulnerable, too much, for the wrong reasons or at the wrong time you will loose the respect of your partner and soon after there love.
Most people seek emotional support, resilience and trustworthiness from their partner, and being excessively "vulnerable" can definitely hinder you from playing that role effectively. This is what can sometimes be experienced as a loss of respect. What you really want is to show a mere modicum of emotional vulnerability that your partner can then have some opportunity to empathize with, and not view you as overly brittle. But not more than that.
Why are you assuming that someone who sensibly refrains from overly impulsive behavior wrt. showing their emotions (this is what "self-monitoring" ultimately means: we all do it in all sorts of social contexts, and it's a normal part of being a healthy, well-adjusted person) must necessarily be "disconnecting" from them altogether and lacking in emotional resilience?
If you manage to "self-monitor" all the time, and never show more than a modicum of vulnerability, that seems very disconnected to me.
Perhaps 'disconnected' is the wrong word, but what I mean is that emotionally healthy people feel their emotions and express them, not just hold them at arm's length and pick and choose which to feel and express.
On the contrary, part of being a well-adjusted person is learning how to express any emotion in a gradual and controlled fashion, without letting it dominate your behavior in dysfunctional ways. As the ancient philosopher Epictetus famously put it: "If anyone were to deliver your body in public to whomever he wished, that any passer-by might do as he liked with it, you would certainly be angry and indignant. But that you should then set your mind at the mercy of all the world, to be troubled and disturbed whenever anyone should happen to revile you--are you not ashamed of that?" In a way, this is at essence the underlying tension that's inherently in play whenever someone advocates for "vulnerability".
Right I forgot we are on HN where we even need a scientific paper on "do women like weak vulnerable or strong confident men?" because nobody ever goes outside.
I bet that people who advocate for showing "vulnerability" are modeling this as a facet of strong confidence, and not opposed to it. But the thing is, if you really have reached the level of effortless confidence where that's a realistic prospect, you won't need that advice! You'll just be able to intuitively calibrate how much "vulnerability" to allow others, as a direct outcome of that strong emotional stability. Most people would probably be better off being told to be a little bit more guarded about their emotions.
Not really, it's just that most of us are adults who have experiences with healthy adult relationships. "Is my partner going to leave me if I display emotional vulnerability" is not really a concern in healthy, adult relationships.
Differences between men and women are down to the situation.
Sometimes the long situation. When a situation has lasted a long time, it sticks, and turns into culture, gender roles.
When a situation has lasted a really long time, it sticks hard, and becomes biology.
But most of the time, it's neither culture or biology which decides what men and women do. It's the immediate situation.
And even if you think it's culture, even if you think it's biology, if you don't like how men are (or how women are) you have to start with changing the immediate situation. The others will follow - eventually.