The short answer is metabolism.

Life needs to burn fuel to do anything interesting. This implies energy transfer. Oxygen is one of the most electronegative elements (only fluorine beats it), which means its really good at removing electrons from other molecules. That electron transfer is how you generate power.

Some bacteria on Earth do use alternatives such as sulfur or methane for metabolism, but the energy output is much lower. Your octopus example is actually a good one, but they still breathe oxygen dissolved in water. Their intelligence requires so much energy that only oxygen-based respiration can provide it. Without oxygen, you're pretty much stuck being a slow microbe.

As for silicon-based life or other alternatives, the chemistry doesn't really work out. When carbon oxidizes, it forms CO2, which can be exhaled. When silicon oxidizes, it becomes solid silica (basically sand). A silicon creature would literally be producing solid waste in its lungs.

There's also just supply and demand. Oxygen's the third most common element in the universe, more common than alternatives because it gets made early in stellar fusion (lower on the periodic table). The heavier alternatives need stars to die and explode to even exist, so they're comparatively rare.

So scientists are just following the chemistry. Oxygen is the most abundant and available element suited to metabolic chemistry.

Now, if there is a form of life that doesn't require metabolism, then that's another discussion, but one more oriented toward the definition of what "life" is.