Why do we revere logic?

I understand it’s use, I do. Sometimes linear, definitive, purely objective thinking is exactly what the moment needs.
But every moment?

(I have a lot of thoughts going on in my mind, I’ll keep them in there because I don’t want to bore, and I want to hear others’ thoughts.)
I will say, though:
That our brains are these huge, amazing, complex organs, and just one part is the logic center. Why does society seem to so value that one part, rather than the entirety of our minds’ potential? Why is, generally, emotionality considered irrationality, and ideas that can’t be step-by-step proven/explained in a linear fashion considered inferior?

Thoughts? ..Any thoughts..?