Rules-as-written, the spell makes you capable of breathing water, not oil.
RAI, Rule of Cool, Good GMing, Storytelling, Game logic, Happiness, Fun, Wiz Biz, Awesomeness, rewarding inventiveness, etc
There's pretty much no reason other than RAW to refuse to allow the Water Breathing spell to affect all liquids. Sure, water has oxygen in it gills la la but it's a magical spell and I don't expect wizards to understand that stuff. They'd just make a spell that lets you breathe liquids.
Basically, if a GM disallowed this at a group I was in, I wouldn't be back. If you're that invested in RAW and that not-invested in storytelling, it's a massive red flag, like the one that used to be over the kremlin. Just huge. There'd be no point continuing to play that game, because fighting monsters for xp is a very small part of the fun of ttrpgs, and if someone is that invested in the rules and that not-invested in an interesting story, the vast majority of the fun is absolutely drained away.
But he's a full caster so you should enforce RAW on him as hard as possible!
This attitude is really terrible and kills fun. All it forces a caster to do is use the laundry list of win spells to be horrifically powerful while perfectly RAW, instead of trying to use spells in interesting (weaker, invisibility is a 2nd level spell) ways, and be more like a storybook magic user than the dnd 'I stand in middle of party and kill everything with glitterdust' wizard.