The first two components of EI are self-awareness and self-regulation—basically how to lead yourself. Mastering your own world comes before leading others. To be self-disciplined, to have the ability to stay focused on goals, and being able to manage stress well—these come out of those two. You have to mobilize your discipline and a positive belief system to keep going when things get tough.
Then there is empathy, or social awareness and relationship skills. You have to be aware to what another is feeling. You have to tune out a range of emotions to sense what another is going through. Full empathy is absolutely crucial for leadership. Without empathy you will be poor at managing relationships.