Comparing Luffy and Kizaru here is a false equivalence.
Luffy has already shown and had both CoC and ACoC explicitly confirmed during his fight with Kaido. So if he didn’t show the usual ACoC effects in Egghead, we can simply say he wasn’t using it at that moment, because we already know for a fact that he has it.
Kizaru’s case is completely different. After Sabaody, Marineford, and an entire fight against a Yonko in Egghead, he still hasn’t shown even basic CoC. He has never knocked out fodder with it, no character has ever acknowledged him as a Conqueror’s Haki user, there has never been any confirmation whatsoever, and he definitely hasn’t shown the advanced coating.
Saying, “Kizaru might have just chosen not to use it too,” is circular reasoning, because you would first have to prove that he even has it. You can’t use the fact that he has never shown it as proof that he secretly has it but simply chose to hide it.
Luffy not using an ability he is already confirmed to have is a choice.
Kizaru not using an ability he has never once been shown to possess is simply a lack of evidence.
And claiming that Kizaru has ACoC is even more ridiculous, because before giving him the advanced version, you would first have to prove that he has basic CoC in the first place.
Could Oda reveal in the future that Kizaru has it? Sure. But a future possibility is not current evidence. Based on everything the manga has shown so far, Kizaru does not have CoC or ACoC.
"And claiming that Kizaru has ACoC is even more ridiculous, because before giving him the advanced version, you would first have to prove that he has basic CoC in the first place."
This is just unnecessary yap though, if Kizaru had CoC him having adv coc is a given, it's just common sense. Because "adv coc" is just applying the concept of ryuou to conquerors haki in order to make use of it.
If you're so adamant on saying "No coc, let alone adv coc" you can also essentially say Kizaru would not be able to break out of the cuffs that yamato was in, because he hasn't shown that kind of haki application.
It's just nonsense. Logically you'd expect an Admiral to have an advanced application of armament. And if they had CoC, they would then know how to apply that application to their Conquerors haki. This isn't the admiral show, these are established characters that have already gone through their progression, they aren't shounen protagonists that still have to figure it out.
The only time we see them having to learn anything is through a flashback which shows how they got to where they are today, like Aokiji's training with Garp.
Can you seriously imagine Kizaru seeing adv coc and like kidd going "what is that haki?"
Kizaru wasn't surprised when Luffy used it. Instead he bragged about his defence.
So when you make that kind of statement, it's like you're trying to make a very reduced and basic version of logic, that lacks knowledge of the context of the series you're talking about. "A has to be proven first before even B" you wouldn't even need to make this statement when you understand the series.
Also it's not even the case, you can logically claim an admiral has adv coc via what i've already explained, and that already entails the statement "an admiral has basic coc" an admiral
doesn't have to show base coc by knocking someone out
and then adv coc, again they are not a main character like luffy who has to show the base version first in MF.
They can literally just show adv coc straight away, which would
be expected given how far we are into the series.