Are a lot of people fully aware that the OP seems to only be talking about the subclass abilities?
Paladin's don't use their Channel Divinities very often, he'd still have plenty of effective spells to prepare, the only actual ability he'd lose out on on a regular basis is the the 7th level pursuit ability.
Now, I also don't think I fully agree with the DM, because your paladin under this interpretation has a hard time declaring new " Enemies" to pursue, while realistically, the same rage and fury that inspired you to pursue your first evil, may be found against other evils that you come across. This sort of thing is clearly best done as a player choice, so that the player can choose when is an appropriate time to change their stance.