There are two reasons why B’s interpretation is wrong. (In the end they are the same thing)
It is obvious that not every single Asian is smart. If I am not seriously mentally impaired, it is obvious that I know that. So why would anybody assume that when I say “Asians are smart”, I mean that every single one is?
Although logically correct, this interpretation does not make any sense in vast majority of real cases and is useless. Therefore, another interpretation should be used instead that that would be meaningful and useful. That interpretation is that the statement is true for a significant part or statistic**.
To show it on the example: we can assume that the general statement (“Asians are smart”) does not mean it is true for every instance (“every single Asian is smart”) as B did, as that is out of reality. Instead it means that it is true for a significant part (“most Asians are smart” or “In average, Asians are smart” or “The ratio of smart people is higher with Asians than some other group”) — which is the meaning that A intended.
Sometimes we really want to say something about every single instance. But in that case we can say it explicitly — “All Asians are smart”. But even in many such cases we can assume that the person is just intentionally over-exaggerating. It is all about trying to understand.
So to sum it up — when somebody says a general statement, they most likely do not mean all/everybody. Just try to be positive — first try to understand what they mean and what makes sense***. People usually mean well. It can avoid a lot of bad things happening.
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* The reaction seems to depend on what the general statement is about though. Saying “Africans have lower average IQ” is quite guaranteed to invoke the response “You racist, how can you say that ALL Africans have low IQ?” at the least — while saying “ALL white males are privileged Trump voter racist sexual predators” seems to be fine.
** Does not even have to be a majority. With “Fish live in water” we mean pretty much all of them. But “driving is dangerous” does not mean we have an accident on most drives, only that the danger is somehow statistically higher than some other activity.
*** Applies even to stupid people. They can mean it the wrong way, but everybody should get a chance first.