I'm quoting from University College London website. Feel free to tell your friend to take a look at it [ Pronouns @ The Internet Grammar of English ]so that you might win this argument :
The first set of forms (I, you, he...) exemplifies the SUBJECTIVE CASE, and the second set (me, you, him...) exemplifies the OBJECTIVE CASE. The distinction between the two cases relates to how they can be used in sentences. For instance, in our first example above, we say that he can replace John John got a new job ~He got a new job But he cannot replace John in I gave John a new job. Here, we have to use the objective form him: I gave him a new job.