Secondo "L'italiano senza errori": Il pronome "te" è usato come complemento oggetto o indiretto; attenzione quindi a non confonderli; non diremo mai: "io e te andremo al cinema stasera" ma "tu ed io andremo al cinema stasera".

I have the same question. Maybe there is a rule where, when you say I and [something], [something] is treated like an object?

My guess is, this is similar to "you and I" vs "you and me" vs "I and you" in English. "You and me" is grammatically incorrect but perfectly acceptable, while there is nothing grammatically wrong with "I and you" / "io e tu" (putting yourself in the second place is just a matter of good manners), it simply sounds ackward because it is never used.