Quick question: Is English your first language? Because there are a lot of subtle distinctions in English that are not obvious - and you might have tangled yourself up in one of those. If we look at the Meriam Webster,
insincere is another way of saying hypocritical.
Sincere on the other hand has, as a first definition, honest.
Quick question in return: are you familiar with the concept of irony? I ask because you're displaying it here in your lack of command of the English language.
For one thing, the most authoritative dictionary of the English language is the Oxford English Dictionary (OED), which you failed to cite. If you check its definition of disingenuous (Second Edition, volume four, page 784), you'll find that it doesn't break it down into numerical listings (dispelling the notion that one can somehow "rank" the definitions of this word), noting that not only does it list "insincere" as part of the definition, but that it can be applied to "persons
and their actions." Emphasis mine here.
Now, if we look at "sincere" itself (OED 2nd edition, volume fifteen, page 508), we'll see that it does have definitions broken down by numbers, and that 1b is "true, veracious;
correct, exact." Emphasis mine again.
In other words, before you question someone else's command of a language, make sure you're up on your own.
Being sincere is not about whether the statement is actually true. It is about whether someone genuinely believes the statement they are making.
Already proven false; see above.
If someone genuinely believes that the earth is flat then they are being sincere when they say the earth is flat despite the fact that it is not true. If someone on the other hand believes that the earth is flat and claims that it is round because they will be given money for that that is insincere - it is dishonest and the opposite of what they believe. This is still true despite the fact that the earth is not flat.
One can judge the sincerity of a claim in and of itself, since as I've already demonstrated, sincerity can be in reference to its correctness.
(Note: According to The American Heritage Dictionary there is some confusion about the meaning of disingenuous and the word may be shifting although your claimed usage is not in line with any standard possibility - but once you accept insincere as an accurate summary you are removing all doubt.
Demonstrably false, unless you don't think that the OED is "any standard" of English.
That you are accusing [MENTION=42582]pemerton[/MENTION] of not believing what he is saying. Which is entirely different from making a mistake.
Again, demonstrably false.
That insincere doesn't mean that and disingenuous doesn't mean that. Both mean that the person that is being accused of such doesn't believe what they are saying. There is a huge distinction between lying (someone knows something to be false and is making things up anyway) and mistaken (someone believes something to be true that isn't). You are not, as you think, accusing [MENTION=42582]pemerton[/MENTION] of being mistaken. You are accusing him of knowingly lying. And accusing someone of knowingly lying is a personal attack.
As I've already demonstrated multiple times, I never once accused pemerton of lying - a statement can be disingenuous because it lacks sincerity, which means that it lacks truth, as a quality of the statement itself. For you to suggest otherwise means that you are, at best, tragically mistaken. At worst, it means that you're deliberately misinterpreting my previous statements in order to manufacture outrage over a non-existent accusation.
I will, however, do you the benefit of presuming that you're simply misguided, rather than having ill intent. I won't even insist that you apologize, which is a good deal more gracious than you've been thus far.
If you are accusing him of being insincere or disingenuous then either you are accusing him of knowingly lying, in which case you are making a personal attack, or you are not saying what you think you are saying, in which case you owe him an apology. Which is it?
Neither, as I've clearly shown. Hopefully, you've learned from your mistakes here, and can let this sordid tangent go.