The reason “shorter than I” is the correct form is that “than” acts as a conjunction here, linking two clauses. If we were to write out the full sentence, it would be “shorter than I am,” but the verb “am” is often dropped and understood in informal use.
On the other hand, “shorter than me” is something you’ll hear more often in everyday conversation. While it’s widely used, it’s not as grammatically precise because “me” is an object pronoun, and there’s no verb in the second part of the sentence to support it.
Than me = Less correct; informal; Less formal
Than I or I am = Correct; Formal
—-Jahani—-