Why can't you be vulnerable publicly? I believe that's strong not weak. Someone like Paul here on the forums is a very strong person. Vulnerable =/= weak.
Because people will take that vulnerableness and use it against you. No one's saying to never be vulnerable. You just have to be vulnerable to the people you're close to and can trust. Not to strangers online or to corporations who will take your insecurities, sell them online, and next thing you know you're getting your e-mail spammed with anti-depressant scams.
It has nothing to do with being strong or weak; it has everything to do with being smart and choosing to not expose yourself to total strangers.