Emotional Intelligence has become popularized by the prolific writing of Daniel Goleman. In his 1988 Harvard Business Review classic, he outlined the concepts of self awareness, self regulation, motivation, empathy, and social skill. It has caught on because the concepts are very effective for becoming a stronger leader, and Goleman advocates they can be learned.
There is also a lot of interest and writing on the idea of authenticity, criticizing those who are somewhat robotic and don't show their inner colors. Of course, it is a lot more complicated than this, but are showing emotions healthy or not?
It depends on what kind of emotions. When one blows up in anger, that often is a pretty negative emotion on those around. When one shows respect and interest in another's feelings, that generally brings about healthy dynamics. In my opinion, Goleman's construct is a good one, but it is helpful to think it through from a strength based leadership perspective.
In strength based leadership, fatal flaws must be addressed. Erratic behavior such as anger outbursts can undermine everything else. Self awareness and self regulation do indeed help control these negative emotions. Lacking empathy and social skills can equally be a fatal flaw in trying to get others to follow. People follow because their personal needs are satisfied in some fashion, and how can you get them to follow not knowing what their needs are? Thus, empathy and social skills are facilitators in this process.
Of course, when empathy and social skills are already your strong points, then further building on these strengths can be very valuable. The key is that you only have so much time and effort to spend on self development. Unless there are fatal flaws, then building on strengths will be of greater value. Working primarily on weaker areas, tends to bring about an averaging effect as strengths languish ... unless of course the weaknesses are fatal. Thus, use teammates who have strengths in your average areas to give you a reading on how your impacting others. Leadership is not a standalone endeavor.
So learning self awareness, self regulation, empathy and social skills facilitate the management of emotions. But authenticity comes from real passion. This is highlighted in Goleman's concept of motivation. However, one doesn't really learn passion.
In my opinion, passion is an outgrowth of personal purpose, what you really want to be and the legacy you want to leave. In that respect, personal purpose requires some real introspection. A helpful way to determine your passion is to look at three primary areas of your life: job development, self development, and social development. Where are your priorities and what do you really want to accomplish? What job turns you on? What physical, intellectual, and spiritual aspects of your life are really important? What do you want from your relationships? If you spend some deep thinking on this, you will find your passions.
Passions drive visions of where you want to go. Now you have the potential of inspiring others to follow if it fits their needs too. This is the real centerpiece of leadership and creates a lot of the authenticity followers seek.