It's called, "sour grapes," or for the psychologically inclined, the perhaps related, "cognitive dissonance."
From the fable, "The Fox and The Grapes."
"Common cope?" I'm not a grammar specialist; but, I think, 'cope,' is only a verb, not a noun. "Compensating," though not very technical a term, would probably be more accurate and possibly more grammatically correct. As in, "She carries a small purse to compensate for her big ego."
or
"...Men, who are unsuccessful romantically, often compensate by taking up nihilistic positions and view points..."
Having sour grapes is a pretty common phenomena. Intellectualizing can be a common way of compensating for lack of whatever and what have you. I do it quite often... heh..
--edit: and cope can be a noun... I still think good old fashion compensation beats woo-woo-new-age-psychobabble any day of the week though.
Now who wants a hug?
--edit #2: ahh, but, 'to cope,' as a verb, is not the same as the various definitions of, 'cope,' the noun!