Why is it always called "the Pfizer vaccine" when it's clearly a joint operation between Biontech and Pfizer with Biontech being the inventor of the vaccine and Pfizer being the pharma giant that is able to help with resources and producing it at scale?

Because Pfizer has a marketing department many times bigger than all of BioNTech.

Because the vaccine is manufactured and distributed by Pfizer, so that's who you buy it from and that's what it says on the packaging.

Easier to say. Just like "Oxford" vaccine instead of "Astrazeneca/Oxford".

GNU/Linux please.

this escalated quickly

That’s essentially the opposite situation, though. Presumably Oxford has better PR people than BioNTech. It also has the great advantage of being easier to spell.

But in this case it's the BioNTech vaccine then.