... (or EQ) is not a thing.
Daniel Goleman, a journalist, manufactured the concept and the culture took it and ran with it.
When people discuss Emotional Intelligence, what they are really talking about is "Agreeableness", one of the Big Five personality traits.
The reason EQ (or Agreeableness) is not a measure of intelligence is because the opposite of Agreeableness--Disagreeableness--can be hugely important and beneficial for a person and for society at large.
For example, the progress of science needs and relies upon disagreeable people.