Using the term "people" or "men" or "women" without a quantifier is misleading. I could say "people think the earth is flat" and it doesn't matter if it's one person or one billion people but the difference is very important.
If I say "people have two legs" and you reply saying what about amputees, that's a debate tactic, not a misinterpretation. If I say "people are amputees" that would be a false statement.
> I could say "people think the earth is flat" and it doesn't matter if it's one person or one billion people but the difference is very important.
The term "people" by itself means people in general. Not all people, and not one person in a billion.
English is neither a mathematics nor a programming language, and should not be treated as such.
I can't help but conclude you understood me perfectly, and are just being argumentative.