Even after I understood why people asking me if I’d eaten, I was still confused about why I kept getting worried looks if I said I hadn’t. In fact, this expression is very similar to “how are you?” in English. Typically, people respond with “吃了(chī le)
– I’ve eaten”, no matter whether or not they’ve actually eaten, in the same way you’d say “I’m fine thanks” even if you weren’t actually feeling great.