If that drawing flashback is one example of an ongoing pattern of how Chia treated Chie alongside the MC all throughout her childhood - I can see why she would be bitter, I think.
I don't think there's any malice on Chia's part in asking her sister to deliver lunch since she'd be at the same school building anyway, but if there's continuous history of the little sister being sidelined/ignored/upstaged and all in favor of the MC, then her resentment is at least understandable, if not necessarily justified (since there's also a chance she's never spoken up about it with anyone, and simply let her feelings fester).