>why are we so obsessed with oxygen when we only have proof that it works for us?

The Copernican Principle: the Earth is not the center the universe, and we humans do not occupy any special place in it. Since there's nothing special about us, then any particular trait of our biology is most likely to be common rather than rare or exotic. Since we breathe oxygen, it isn't because oxygen breathing is rare, but because it's common.

It is an assumption, yes, but your assumptions are more likely to be correct (or closer to correct) the less dependent they are on rare or exotic conditions or properties.

Also, since the only forms of life we have any experience observing is the kind that occurs here on Earth, the easier it will be to recognize life elsewhere the more closely it resembles life here.

That's not to say other chemistries which sustain life are impossible, but it will probably be harder for us to recognize them as life the first time we observe them.