Knowing when to be authentic in allowing others to see your emotional sensitivity and when to set that aside separates the mediocre leaders from the truly great ones.
I was watching Ken Burns' TV series Civil War and was surprised to see that Ulysses S. Grant was both resolute in his ability to lead his troops into tough battle situations and showed a seemingly incongruous display of emotion (deep sorrow) when he lost valuable leaders that died in battle. Grant even broke down once and sobbed uncontrollably over the loss of one of his generals.
Too often today, we view emotional sensitivity as a weakness. Quite the contrary, for leaders who know who they are, sensitivity is an incredible well of strength (that other insecure leaders don't have) they can draw from in tough times. The most dangerous leader is one who acts like he is never sad, angry, or depressed and puts on a macho mask. All of us struggle with emotions, and those who make peace with them and their creator are the most generous, gentle, calm, yet resolute, direct, honorable, and courageous people you will ever meet.