Rival Rematch switching pokemon

So I was fighting Blue in the champion rematch. Is he actually able to switch pokemon? I was fighting in and even managed to get him down to struggle while he had 4 other pokemon remaining and he refused to switch. It was also a Shedinja that I had out and pretty much anything other than his Venusaur has the ability to hit it for super effective damage which is why I'm questioning why he wouldn't switch Alakazam after running out of Shadow Balls.

Right now the only thing I can think of is the fact that because Alakazam has Shadow Ball he just keeps it in even though he has run out of PP on the move.