China consulate in Florence? Do I need Italian ID card?

I think the visa office of the consulate in Florence doesn't know the rule: An applicant holding a passport other than Italian passport should provide the original and a copy of his or her permanent residence or work permit which should be valid for at least half a year (except for those who enjoy visa or permit exemption for residing or working in Italy).

You are a EU-Citizen and stay in Italy, I don't think you need the Italian ID card (a kind of residence permit in Italy) for studying in Italy.

You can explain to the visa officer that you don't need the Italian ID card for studying in Italy because you are a EU-citizen and Italy is a EU country.