Evil Vegeta said:
The fact that this was his maximum (he wasn't sure if he could do a 20x increase)
Let's start by demonstrating that this is a fallacy. Goku not being sure he could resist the KKx20 doesn't mean the KKx10 is the maximum he could achieve, because between the KKx10 and the KKx20 there are 9 intermediate levels of KK.
The fact that he tried the KKx20 means that he could surely reach the KKx15 somewhat comfortably at the very least. By the way, going from KKx18 to KKx20 would already be your usual mid-fight power up, so with a bit of context it's not difficult to guess that before knowing about Freezer's strength Goku thought a KKx12 or KKx13 would be the maximum he would've needed.
So your fallacy: you act as if the KKx11 to KKx19 doesn't exist and can't be used under any circumstance. Only then your reasoning saying "if Goku wasn't sure he could reach the KKx20 it means he couldn't go further than KKx10, and that means that when he told Freezer he could increase his strength even more he meant going from base to the KKx10 because he wasn't sure about the KKx20 and the KKx11-19 doesn't exist" becomes true.
I don't know why wouldn't the KKx11 or KKx12 exist. We saw the KKx2, KKx3 and KKx4 in the earth, and in Namek Goku used the KKx2 (against Ginyu), the KKx10 and the KKx20 against Freezer. Does that mean that the KKx5 wouldn't be possible for Goku even if he wanted to use it? Why would the KKx3 or KKx4 exist and not the KKx5 or the KKx11. They obviously were possible, and Goku obviously took them into consideration.
Evil Vegeta said:
the fact that Freeza said he was holding-back a lot of power, and the fact that Goku agreed Freeza was right shows he clearly wasn't.
Of course, if Goku could go as far as to use the KKx20 and he was already using the KKx10, any level between the KKx10 and the KKx20 Goku could reach if needed would already be a huge increase in power. A 10-20% difference in DB is already a big increase in power, so Goku fighting at 50% the maximum strength he could achieve is him holding back a lot of power (a lot more than in any other fight Goku has ever fought).
Evil Vegeta said:
The only way to reach another conclusion is by twisting the dialogue and adhering to strange logic.
Yes, to think that Goku could use the KKx11 or KKx12 in case of need is only possible by twisting the dialogue and adhering to a strange logic. It's much more logic to assume that once you reached the KKx10, the only KK possible going from there is the KKx20 (I disagree).
So my "strange logic" is that when Goku said he could become stronger it's because he clearly had bigger levels of KK he could use in the fight.
Now, let's demonstrate why the KKx10 wasn't activated in the middle of the fight. Let's say the KKx10 was activated here because Goku has an aura (even if his black eyes already demonstrate that this is not a KK aura, but let's assume that Toriyama made a typo on his drawing and that this should have been a KK aura):
http://mangalife.org/read-online/Dragon-Ball-chapter-118-index-2-page-10.html
Then, that forcibly means that the KKx10 is not activated in those pages:
http://mangalife.org/read-online/Dragon-Ball-chapter-118-index-2-page-6.html
http://mangalife.org/read-online/Dragon-Ball-chapter-118-index-2-page-9.html
http://mangalife.org/read-online/Dragon-Ball-chapter-118-index-2-page-14.html
http://mangalife.org/read-online/Dragon-Ball-chapter-119-index-2-page-1.html
That breaks any kind of logic the fight could have and every single rule the manga had established until then and from then onward. So, Freezer is hitting with enough strength to damage Goku while using the KK10, but then suddenly Goku can also resist those hits without the KKx10?
What kind of logic can explain this? Or freezer detects Goku's strength and constantly goes from 50% to 5% of his strength to not kill Goku (which doesn't have any sense) or Toriyama screwed and made a "this is Toei and I don't care about my work's consistency any more".
Not only that, but Freezer would also break another implicit rule of the manga regarding the surprise attacks. Never before a 10x increased could be anticipated like this. In fact, even much, much smaller increases (Freezer going from 50% to 70%) were enough to catch much better fighters by surprise. And now Freezer suddenly anticipates a 10x increase?
The fight becomes absolutely incoherent no matter how you look at it.
By the way, when Kaio says that Goku IS ALREADY USING THE KKX10, if you look at Goku in those pages,
he doesn't have an aura.