Illiteracy is the lack of knowledge and understanding. It is a sort of imperfection that cannot be part of the prophet's personality. The messenger of Allah was - without any doubt - aware of all what he needed to prove and support his message. The huge amount of information and knowledge that were spread in many narrations is sufficient to prove such a truth. Imam Ali was referring to such enormous knowledge when he said: "the messenger of Allah taught me a thousand doors (kind) of knowledge; each one of them opens to a thousand more doors".
Not being able to read is not a deficiency since reading is a way people use to gain information and knowledge and the prophet (peace be upon him and his holy progeny) did not gain his knowledge throughout studying and learning but rather got them directly from Almighty Allah.
