Your body is devoting a lot of energy into healing itself, so digestion and appetite don’t take as much precedence. As previous commenter mentioned, you can go to around 2 weeks without food. The same reason for why you shouldn’t drink milk if you’re sick, it’s not being digested as fast so it’s sitting in your warm stomach and spoiling—and then you throw up. (At least from what I understand)
Edited to clarify
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