No, it just made you wrong, and if you are wrong about the basics, a logical reader will assume you wrong about everything else (unless proven otherwise to a higher standard).
That's the thing with generalizations - they're simplified models with imprecision, not necessarily wrong. And if someone uses a generalization like "all people who use generalizations are irrational and wrong", that tells you something about their own reasoning capability.
If you used the fact that you personally lived outside the US to claim that Americans do not live in America, you are far more wrong than the generalization is.
And you are creating a strawman in which I make a stupid false dichotomy.
Not all Americans live in America. Is that a generalization?
Yes, in that's a general statement about what all Americans are doing. But to say that it makes "Americans live in America" wrong is not quite right, either.
Wiki claims that American diaspora is estimated at 3~6 million. Out of an American population of 300 mil, that's 1~2%. So "Americans live in America" is 98% true. If you want to say the statement is wrong, it's 2% wrong, 98% right.
If you're going to try to force people to always say "the majority of American live in America" or "98% of Americans live in America" instead of "Americans live in America" every time it comes up, you're being pedantic for the heck of it.
Generalization is necessary to communication. Every topic has a nigh infinite number of details, and the choice of which level to discuss it at is arbitrary.
It's not irrelevant. It points out the inanity of the claim.
My point is that it is justifiable to use generalizations when they are true, or mostly true. I used an inane generalization just to get something that would be 100% correct, or close to it. The existence of manboobs does not change whether or not the statement "Women have boobs" is a generalization.
Cats don't have boobs, though they do have mammaries. Bad generalization of boobs you used there. If you got that one thing wrong, do we need to disqualify 100% of what you say?
Because if we applied the "modern feminists are not rational => generalization => bigot => irrational => IGNORE" chain of logic, apparently yes.