Your analogy about murdering someone vs. not murdering them doesn't seem to apply. Google's CEO reportedly debated about the decision with his direct reports [0]. By Monday, they had apparently decided that the memo indefensible and a clear violation of the code of conduct.
If the CEO has reached the conclusion that Damore is guilty of a fireable offense, what is the purpose of waiting? Unless he had doubts about the merits of the case, or he thinks Damore should be given one more chance to make a pubic apology, or he thinks Damore should be given a week to clean things out and make peace. All of these things would require waiting, which means that waiting is not a neutral opinion about the case or its perceived urgency.
If I see someone and immediately shoot them, I'd be in trouble because I don't have a good explanation for why I acted immediately.
If I see someone from 100 yards charge at me brandishing what could be a weapon, waiting some time before shooting is reasonable, but waiting for too long is foolish.
If someone walks towards me carrying what looks like a bomb, and then tells me that he is in fact carrying bomb and reveals to me its bomb-like features, and then tells me he's going to detonate the bomb at a playground 100 yards away as he starts walking to that playground, my decision to wait becomes an even more of an opinionated, non-neutral decision.
Again, just because I think that acting immediately was not irrational doesn't mean that I think Google handled things remotely well. They may have handled things in what logically seemed like the least fucked up way possible, given all the other fuckups that were all allowed to accumulate.
Since this is apparently grounds for termination, what would be the point for waiting between deciding the verdict and carrying out the sentence? Unless the Google CEO had doubts, or that he thought Damore could apologize and save face given the opportunity, or that
[0] https://www.recode.net/2017/8/10/16125452/google-sundar-pich...
I never said they were being more rational, I don't know why you keep arguing that straw man.
More importantly, their rationality is less important because they weren't demanding someone get fired. When you're demanding someone be fired the burden of evidence is much higher and it better be fact based and not interpreted.
If you murdered someone you better have a good reason, I'm not interested in your reasons for not murdering someone and whether they are rational or not.
I also hold the CEO making a formal statement to a much higher standard than an employee writing an internal document. Damper was a cog in a machine, Pichais statement is going to have some big ramifications within Google and possibly much wider.