When you pick your starter in Red/Blue/Whatever:

*your character* obtained *starter*!

Blue: I'll pick this one then!

Blue obtained *starter super-effective to you*!

You: Uurgh I hate Blue because he chose the Pokemon super effective against me

LATER IN THE GAME

*NPC* is about to send out *Pokemon*. Will you change Pokemon?

You: *selects Yes* *switches to the Pokemon super-effective against the NPC*

So all Blue, or any rival, really, did was what you'd do later in the game.