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.

I think you're working too hard to be pithy and are therefore forgetting to actually communicate.

What are some things that make a man seem vulnerable?

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.