Emotion and sensitivity are two very different skills. Being emotional or being sensitive will provoke very different reactions in me and around me.
An emotion, an emotional reaction triggers strong feelings in me, either a joyful feeling or a sad feeling. In both cases my judgment will be shaken and I probably won't react in a balanced way, either over-reacting with exuberance or with wailings and counter-attacks. I react emotionally when I take things personally, when I feel attacked personally or when I feel flattered. In both situations it is probably not the end of it: instead of discussing the subject at hand, I will focus on my self-defense whenever my person is questioned; when flattered, I'll probably wonder why the other person says these wonderful things about myself or I'll feel encouraged to prove that I deserve those compliments instead of discussing the matter itself.
In order to understand what happens around us we need sensitivity. Sensitivity is an antenna tuned to the intrinsic state of the partner you are communicating with, whether this be a rock, a flower, a dog or a human being. We are best trained to communicating with humans but we often react too emotionally and not enough with sensitivity. Being tuned to the inner state of the other human being allows us to understand his action or reaction. If we understand, we can't condemn; on the contrary, we will be able to act in a way that allows the person to make a new choice: to act in an appropriate way or to start considering his behaviour. In any case, we must not be involved emotionally otherwise we strengthen and confirm the other's state of mind and we are right in the middle of a vicious circle: it is not really what we look forward to, is it?
Being emotional can be compared with fighting in the front line at war, being attacked by several enemy soldiers at the same time: we are completely absorbed by fighting off the attacks; there is no room for any plan, for any wise strategy.
Being sensitive can be compared to the wanderer who sits on a high rock and who observes all the conditions around him before hitting the road, hitting the road meaning to take action. This action is based at 99 % on observation that has nothing to do with myself. Being sensitive means using my self as an instrument to understand the world around me; I am only ONE aspect among thousands.
So when somebody insults me, I am not going to insult that person but I'll sit on a high rock and I'll look as deeply as possible in the other person's personality in order to understand what really happens there. This will allow me to distinguish a right reaction from a reaction that would fuel the conflict. Let's not forget that one of the possible reasons of the insult might be that I made a mistake, so I'll apologise sincerely. And a sincere effort to make the best of such a challenging situation always leads to a happy ending. Life is made that way.