if 배고파요 means I'm hungry, why 배 안 고파요 means I'm not hungry?
I mean, why I'm not hungry is 배 안 고파요 because if we follow the rules it should be 안 배고파요, shouldn't it?

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배 안 고파요, 안 배고파요
both are okay in conversations.

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"안" is put inside the verb of hungry because "배고파요" is not literally I'm hungry, but "My stomach is craving to eat". "배" is stomach and "고파요" is pretty much hungry, so "배 안 고파요" Is literally "Stomach not hungry".

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I'm hurry means 배 고파요.  but Korean usually  say that except subject.