[user104658]

It depends on what you mean by emotionally vulnerable to be honest. If you mean being emotionally fragile, then it is obviously a bad thing. If you mean offering up emotional vulnerability as opposed to being "stoic" / un-emotional / closed off... then being able to be emotionally open is always going to be preferable.

A strong person is a person who feels, who admits that they feel. Who can experience the whole range of human emotion without it breaking them. There's a skewed perception that it's better to be "emotionally tough", but to me, that simply means having walls up to defend oneself against negative emotion... and that isn't strong at all. If anything, it's cowardly.