Well the "proof it works for us" is part of why our searches for life (and habitable planets) center on life lthat functions like our own. It's easier to detect and confirm carbon based, oxygen breathing, water drinking lifeforms (especially at a distance) than looking for exotic life that doesn't use those things. As noted in the comments by greypowerOz, there is other reasoning besides that, oxygen is great for metabolic processes and complex life, but other respiratory gases like hydrogen has been considered.

If you're looking for other forms of life, you're really looking for chemical disequilibriums, an abundance of certain elements (like oxygen, and methane) that on their own, would dissipate quickly, and so need some process like life to sustain that abundance. However, false positives are possible, and natural processes could create these same disequilibriums under the right conditions, and look like life. So that's a big thing we need to keep in mind when looking for biosigniatures, especially ones different from life like on Earth.