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Well them as below, your "why" question isn't specific enough to be answerable.
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I managed to answer it in one sentence, and I'm not even an expert.
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Well, inasmuch as most people don;t really pay much attention to the specific difference between mass and weight, that's probably true. But that;s not the fault of science teaching.
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Start the earliest textbooks with "everything is made up of little bits of stuff: atoms" and you've solved it.
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I don't think that's entirely true.
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I do.
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Why what? I don;t understand what you;re asking about. If you put an object on a scale here, and on the moon, the readings would be different. That;s just an observable feature of how the physical world works.
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And extremely unsatisfying, put like that, because you still haven't told us why.
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It all seems perfectly logical to me, except for the existential question of "why is reality like this". We observe things and make theories explaining them.
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It's also a fact that it's far easier to remember "mass is all the atoms added together, and weight is how hard gravity pushes them" than "an object has a certain mass but it is experienced differently in different situations", because the people doing the learning are humans rather than computers. It might be easy for you, but the people having to learn it in schools are little kids, many of whom have no special aptitude for the subject.
It's the same mistake that the big, French daily papers make. They hire these über-intellectual journalists who can craft a technically perfect article that no one wants to read, because it's desperately boring and extremely heavy going, having been written to be read by a robot entirely unfamiliar with human society.
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Well no, it says it's true because it is observably so.
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That doesn't help when you're six years-old and trying to work out how come weight apparently isn't really weight after all.