This is such a common mistake that I’m afraid someday your friend’s use of the pronoun “I” will become acceptable. However, for now, the rule is this: I and me are both pronouns. However, they are used in different situations. I is a subjective case pronoun. Me is an objective case pronoun. “Between” is one of a group of prepositions. And the pronoun you use after a preposition is always in the objective case. So “Brenda and me” is correct.