So in your mind, because one potentially false stereotype fails, most stereotypes can't be false? Outside the US there are plenty of stereotypes about Americans - are all those true?
If they hold any water, yes.
Too many people today are brainwashed by "political correctness".
Think about it RATIONALLY -- why do stereotypes refuse to die?
People make wrong assumptions based on stupidly small and biased samples. You are a good example of this. You don't know all stereotypes, in fact it's likely you only know a small fraction of stereotypes and that fraction is biased by geography and self-selection and generally poor education in statistics and/or logic (i.e. not understanding that even if most avid shoe shoppers are women does not imply that most women are avid shoe shoppers). From this you have generalized that this says something about all stereotypes. Not only that but I'd wager you probably don't know many of the true values (i.e. How many Americans really are X).
So how do we cure someone of this? That's actually a complicated question. You seem to imply that as soon as a significant portion of the population exemplifies something contrary to the stereotype then people don't believe that. For which there is plenty of evidence against.
For example racial intellectual stereotypes persisted even in the light of data to the contrary. In some cases due to actual fudging of figures but in other cases it really does appear that these people sub-consciously misinterpreted results. We have records of various experiments done where the results were either clearly ambiguous (favoring no race) or clearly in favor of some other race and their conclusion went actually counter to their own results. So one reason bias persists is a kind of willful ignorance.
Another reason is that people avoid dissonance. Especially people who have a lot invested in an idea. For example, people who believed that the world was going to be destroyed and they were going to be rescued by aliens. When the prophecy didn't come true their leader prophesied that they had been spared and given another chance to save the world. Clearly the evidence was either in favor of the idea that the world was never really going to end or at least at parity with it. What did most of the believers do? The chose to believe that they have been given a second chance.
A third reason is that a lot of stereotypes are phrased in a way that is either unfalsifiable or infeasible to falsify. I think one poster below stated that women aren't as logical as men. If you met one logical woman would that be enough to stop the belief? No, because it's asserting what "most" people are like not all. However given that the person in question will never meet "most women" let alone engage the subset of women he/she does meet in some kind of discussion which can readily deduce if they are "logical" or not relative to "men". The person can, keep their stereotype pretty much forever.
We make all kinds of assumptions all day, every day. You don't always have the time for a fair, objective, in-depth analysis of everything.
The far, far, far, far more rational approach is to simply believe that one rarely has the information to make certain generalizations. This isn't political correctness, it's just math.
I'm sorry, but if were a hiring manager, and there were three people applying for a software engineering job, named Amanda Jones, Deshawn White, and Wolfgang Wattenburg, and I didn't have access to any information than their names, I'd probably do the "un-PC" thing and choose the German-sounding guy. True, he might be the one exception to the stereotype, and the female might be particularly good at programming -- but it's usually smart to go with the odds.
Again, this is a good point about how you suck at math. Your assumption is based on the population distribution of software developers. However that is only useful as long as the sample is random. i.e. picking someone at random from a population. A male is more likely to be part of a profession that is predominately male than a female. However job applicants are self-selected so the distribution no longer applies. Given it's highly likely that the vast majority of applicants to a software development position are software developers (especially if it's not an entry level job) My sample is less than 1% of application are completely out-of-field. The likelihood is that all three are software developers of some kind.
So from there it's a question of ability not if they are developers or not
And remember -- the exception proves the rule.
Normally, I'd deconstruct that to show what a bizarre statement it is.
Just because you can show me a single female computer programmer will not cause me to throw my hands in the air and say, "You're right, there's no pattern. Programmers are male and female." No, you merely showed me an exception, which is remarkable because it's an exception to the rule.
Perfect example of how you can keep your prejudice as long as you like.
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