Well I think that he may be trying to set off an example of what a real trainer is like, and impress her in that way. He wants to look cool in front of his sister. :B But, I still think it's cute that he has one and walked with her. Rival/sister relationship!
Unrelated, but I wish our protagonist had a little brother or sister. Maybe even a sibling that goes off on their journey the same time as us and they would be our pseudo rival.
I really want to find out more about the rival/protagonist relationship and his relationship with anyone though to be honest. :[ It's killing me!