In his seminal book “Emotional Intelligence” Daniel Goleman writes, that in order to understand why reason and emotions are at odds we need consider the evolution of human brain. 

Noting that our brains are nearly three times the size of the brain of our nearest cousins in the evolutionary tree, the non human primates, Goleman states that over millions of years of evolution the brain has grown from the bottom up with its highest center is developing as an elaboration of more primitive, ancient parts (the growth of the brain in the human embryo roughly retraces this evolutionary course).  

The brain stem surrounding the top of the spinal cord is the most primitive part of the brain.  This part of the brain is shared with all species that have more than a minimal nervous system. 

Often this is called the reptilian brain since it has been there from the time of the emergence of the reptiles from the oceans.  It is in this brain stem that the primitive emotional senses reside. 

The olfactory lobe, the part of the brain responsible for the sense of smell is one of the oldest parts of the sensing system of the brain. Since each living being has its own unique olfactory signature, this sense is used to decide what is good (edible, good sexual partner) and what is to be avoided (poisonous food, predator). From this lobe other emotional centers evolved to decide what was to be approached or avoided and then a further layer told the body what to do based on this layer (bite, spit, approach, chase).

This is one of he reasons that the sense of smell evokes memories of early childhood with associated emotions. Also note that this is the least filtered of all senses.

When the mammals evolved new parts of the emotional brain were added as a ring like structure around the stem.  This is called the limbic system from the Latin word for ring, limbus.  Proper emotions (less instinctive) such as, anger, love, and dread, arose with the evolution of the limbic system.  Learning and memory were refined by the evolving limbic system.  Now the animal could compare and contrast an odor with an old one and decide what to do based on learning.  This was done by a thin layer above the limbic system, the cortex.

About 100 million years ago the mammalian brain grew from the primitive parts and developed and on top of the reptilian brain and limbic system a two layered cortex. This cortex includes the regions that plan and comprehend what is sensed and coordinate movement, Later, several new layers of brain cells were added to form the neocortex which added huge amount of extra intellectual capacity.

Much later in evolution from those primitive emotional areas evolved into our rational thinking brain with the huge homo-sapiens neocortex, which much larger than that of any other species. This is the seat of rational thought and allows us to think about what we feel.

However, even in the modern human with our computers, Internet, cell phones and other technological conveniences, under the neocortex, was the cortex, then limbic system with the higher emotion and finally the brain stem with the instinctual emotion.

Thus we should understand that there was an emotional brain long before there was a rational one and thus emotional intelligence is at least as important as rational intelligence or IQ.