Earlier quoted context omitted.
What do they mean by "vulnerability" here? There is this constant redefinition of words. In mainstream usage, "vulnerability" is not a good thing as it means you are open to problems and can easily be attacked. They presumably mean it in the sense of being "open to your own emotions" or tender. Silly misuse of words for a serious subject.
I think you are projecting the sense of the word from computer security onto people. But "vulnerability" always has that second sense in common speech, as in "showing vulnerability". If a person is actually open to being harmed in some way we use the phrasing "they are vulnerable to ...", which has quite a different meaning.
No, definitely not thinking in computer terms. I know the word from a completely different context. I think what they mean is sensitivity (which can be good or bad) and tenderness (which is generally good). But there are contexts in which it is not helpful. We have a problem with street violence where I live, and showing your emotional side to a potential attacker is not the best way of avoiding trouble.