As others have explained, "not that" is a unit. "Not that that" has the accidental effect of putting two "that's" together. There is a kind of language joke or riddle about the possibility of having a correct English sentence in which the word "that" appears several times in sequence. The funny thing is that the sentence really is understandable to a native English speaker--if it is spoken with the right rhythm and intonation. The riddle is: "Can you punctuate this sentence so that it makes sense and is grammatical English?" "He said that that that that that man said was correct." The solution is: "He said that that 'that' that that man said was correct." It's a little crazy but it's possible. Imagine this: Man A: "Thot." Speaker: "That's wrong." Man B: "Thot." Speaker: "That's wrong." Man C: "Thot." Speaker: "That 'that' is wrong, too." Man C: "That." Speaker: "Ah, the first time was wrong, but that 'that' that that man said was correct." Audience member: "What did he say?" Audience member's friend "He said that that 'that' that that man said was correct." Here I've read it aloud, using intonation and rhythm to make the meaning clear. https://vocaroo.com/i/s0MILLW09Ht5

Not that that justifies = Not that this justifies = Not that it justifies = Not observing the fact that that thing justifies = Not acknowledging the fact that the thing we're referring to justifies

First 'not that' is a conjunction that is used to explain that you are not suggesting something. E.g. "She wouldn't tell me how much it cost - not that I was really interested." Second 'that' refers to something that has been mentioned before, so it's used simply to avoid the repetition (as Kai has already mentioned).

"Not that，that justifies treating them badly, of course". "Not that" is one sentence as a whole, "that justifies treating them badly of course" is another sentence as a whole, so don't mix it up. I think the expression means "it couldn't mean he was treating them badly because of that". I am not a native speaker. So let's wait for the native English speaker's opinion. because it could be wrong too since I am not a native speaker. And the word "that" here is referring to the sentence "A general habit of optimism in one person could make them intolerant of a colleague who's constantly pessimistic". English speaker would use the word "that" or "it" to avoid repetition. Also, "not that, that justifies treating them badly, of course" in Chinese means, 不是那个原因他才会那么粗暴的对待他们. have a nice day and hope this helps.