Mainstream society tends to take and promote the view that sensitivity is a kind of weakness and that being kind-hearted and moral is often a sign of cowardice and self-righteousness (on the concept of 'pussy' - as well as 'dick' and 'arsehole' - see earlier post Team America: Dicks and Pussies).
I agree that sensitivity can lead to feeling touchy and emotionally vulnerable but I largely view sensitive people as stronger and more in touch with themselves than hard-nosed, emotionally constipated and repressed 'tough' men and women who often find themselves preaching and acting philosophies of hate and stigmatisation that are common currency in mainstream political discourse.
It's a well known truth that bullies often prey on sensitive people but bullies are themselves given to fear of both themselves and natural law and in their self-loathing want to cause others to suffer to make themselves feel less bad about themselves as they express their physical and animalistic superiority over others.
It takes courage to open up one's heart, to oneself and others, for there is always the attending risk of being hurt and exploited since that open-heartedness could possibly be interpreted as a sign of vulnerability and 'weakness' by predators.
Opening one's heart and standing for what you believe in also takes exceptional courage (coeur - rage, courage as anger of the heart, see post Courage) as it goes against the grain of psychopathic culture (which we largely live in) and it is far more cowardly and weak to act immorally and without care, since this is sadly the norm promoted by society, than it is to open oneself up to others and care for them within one's limits, especially when the mainstream media is programming us to hate rather than to love.
So in this, like almost all other areas in my opinion, the mainstream view is a false view and sensitivity, if well managed and leading to being a better, more moral, person, should be celebrated as true strength of spirit since not given to the temptation of preying on others (non aggression principle) as well as encouraging one to speak and act against what is wrong under cosmic law (self-defence principle).
All that being said I know for a fact that I would not do well in a physical confrontation, as I'm far from being a so-called 'hard' man and my instinct is to be 'a lover rather than a fighter' when it comes to such confrontations. I guess that is a weakness that I need to overcome.
To sum up I'd say that immorality stems from weakness rather than strength, contrary the message of many contemporary movies and shows, and the true pussies - if one wants to use that word in its negative connotations - are those who give in to fear-based consciousness with the result that they do harm to others.