I want them to threaten you. Give you setbacks, not just be a nuisance.
Say things such as:
"Your pokemon are cursed with a horrible trainer as we speak... Relieve them of the burden of having to be in your presence and sentence them ALL into the wild."
Or more harsher:
(Just say you own a Charizard and you simply cherish it)
"Your Charizard is unhappy, It is weeping... Crying, thinking that it will be forever depressed knowing that you are its master. Let, it, go... LOOK AT IT! Cant you see the pain it has gone threw? It is suffering! Open your eyes and let that Charizard GO!
"You are useless, you will never beat me, you will never hold any victories against me or anyone, you will always be in the shadow of someone, you are my slave and I am your KING!"
But I don't think many people would enjoy this kind of rival.