Does assertiveness and certain kinds of competitiveness and domination preclude Emotional Intelligence? I don't believe they are mutually exclusive. You can be assertive and emotional intelligence at the same time. I certainly was taught to be (and was naturally) competitive. I was also taught and grokked fair play. Winning by cheating was a hollow victory. The point was not to win but to be the best. I could find satisfaction in a loss where I was the better player but lost do it a fluke or just bad luck. I would fight you with one hand tied behind my back to make it a competitive fight. I love a challenge and have no interest in easy victory.
It took me a while to catch on, first I would let children beat me at some games and then I began to understand that even some adults need me to not try my hardest so that they would have a chance to win. The trick was to not let them catch on that I was throwing some points their way so they would come back and play some more.
Some of the stereotypes hold because of genetics and some hold because of what we are taught. It is both nature and nurture.
TEK