But let's be real for a moment -- the guy was probably not fired because he's a prick. Who knows the reason, but ultimately Alphabet is a public company that demands results (and returns) from assets (companies) it invests in (acquires). My hunch is that Nest (and/or it's subsidiaries) were not delivering, and the CEO is ultimately responsible.
It probably didn't help that the guy is an asshole, but let's not pretend that Larry Page walked through the Nest offices like a white knight, sensed a "negative energy", interviewed the sad-looking office manager, and determined the CEO was "damaging to company morale" and therefore MUST be replaced.
Page is the CEO of the one of the largest and most important publicly traded companies in the world. He has a legal and fiduciary responsibility to do right by shareholders. If the Nest CEO was putting up numbers, he'd still have a job, period, asshole or saint.