Here's why:
* "Me" is the correct pronoun in this case. When used as the object of a preposition (in this case, "with"), the pronoun should be in the objective case.
* "I" is the nominative case, used when the pronoun is the subject of a verb.
To test this: You could rephrase the sentence as: "You met with Scott and me." This makes it clearer that "me" is the object.