Earlier quoted context omitted.
The problem is that the people who thought lynching was fine had the same sense of certainty that you have. Which all by itself is enough to refute the claim that such a sense of certainty is sufficient.
To me, any syllogism which tells me I am not qualified to say that lynching is not immoral is probably broken. Rational argumentation is fine but it requires that we start with some reasonable premises. Like any math problem, if you get strange answers it indicates that you're doing the problem wrong. If you divide the circumference of a circle by its diameter and you get something like 31.4 you might wanna check you…
Yes, but you aren't doing that. You aren't deriving the conclusion that lynching is wrong from some reasonable premises. You're just asserting it. Another poster downthread did offer a reasonable premise, the golden rule, from which the conclusion that lynching is wrong can be derived. But that doesn't completely solve the problem either; see further comments below.
> if you've "refuted" the idea that racially-based lynchings are universally morally impermissible
This claim is already refuted by human history.
> you might really wanna look at your math
You might really wanna consider that ethics and morality are not math. You can't establish ethical and moral claims simply by deduction. You have to get people to agree to them--or you have to impose them on people by force (and then you have to deal with the ethical and moral problem of justifying such use of force). Even if you have premises that you think are reasonable that support your ethical and moral claims, you still have to get other people to agree to the premises. That's why ethics and morality are hard.