I don't want to start a war (teasing.

) but what's confusing or difficult to understand?
Those who are and believe it means what
@Rainman4707 believes it means are focusing on the word "emotional" disregarding the word "intelligence."
Intelligent people (emotionally and intellectually) generally speaking are not overly and irrationally emotional or over-reactive (men or women) and with respect to men who possess EI they certainly won't be behaving like women or taking on the wife role as the OP believes.
The term's purpose is to differentiate it from "intellectual intelligence/quotient (IQ).
Both IQ and EQ are needed in varying degrees to be successful in life IMO.