Because it's the only thing we know that can sustain life

It's true that you can possibly make non-carbon-based life, but we have no idea what any signs of that life would be, so we just stick with what we know what our form of life makes (C02, methane, etc)

We want to find species like us humans, probably thinking it’s easier to set up communications between us and them. Also we’re looking for resources. IMO.

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The simple answer is that if they are different enough from all of the life that we know about that they don’t need those things then it’s likely that we won’t know what to look for to find them. At the distances we are dealing with we can just look for things moving around. We look for planet-wide traits since we can see those, and only know what those traits might be based on our sample size of one living planet.

As a simpler example, say we were using just a telescope to look for trees on Mars. We can’t see a tree from here, but all the trees we know about form big green forests, so we just look for green. There might be other color trees on Mars, but we have no idea which other color they would be, so looking for other colors won’t tell us anything.

We have limited resources, so we can’t look at everything in detail all the time. We have to prioritize how we are looking for life, and we only have one example of where life can be found: Earth. So we look for Earth-like planets because we have positive-proof that life can exist there.

Imagine you were looking for a doctor in a hospital; you’d probably look for someone wearing a white coat with a stethoscope hanging from their neck, right? But anyone in the hospital could be a doctor; the guy wearing skinny jeans and a sweater walking through the lobby could be a doctor coming on/off their shift. But we know that white coat + stethoscope = doctor, so we immediately look for those signs first.

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> water

Liquids are very good at facilitating chemcial reactions, because they're dense, so different molecules spend a lot of time in close contact with each other, but unlike in solids, the molecules can move around freely. Liquid water is especially good for doing chemistry in, because it's a very strong solvent - a water molecule has a positively charged end and a negatively charged end, which grab onto different parts of solid/gaseous substances and pull them into the water.

Liquid water should also be pretty abundant, since hydrogen and oxygen are the first and third most abundant elements in the universe and they love reacting with each other to form water. The range between its melting and boiling points is pretty big, and there should be plenty of planets that have temperatures like that somewhere. So it's not something that's incredibly rare and only found on Earth - it should be fairly common.

People have come up with ideas for substances that could take the place of water, such as ammonia, but all of them are either rarer than water, or less good at facilitating complex chemistry, or (usually) both.

> oxygen

There are plenty of known organisms on Earth that don't require molecular oxygen, and even some that die if they are exposed to significant quantities of it. So nobody assumes that extraterrestrial life would necessarily require an oxygen-rich atmosphere. However, I'm pretty sure that all known life contains oxygen atoms somewhere, and it's one of the most abundant elements in the universe and appears in a huge range of chemical compounds, so it would be a little surprising to find a life-form that doesn't contain any oxygen at all.

> an atmosphere

Without an atmosphere, you don't get any surface liquid or gas. It is possible that life could exist underneath a solid surface though. For example, it's thought that Europa has a liquid water ocean under a thick layer of ice, and it's not implausible that life could emerge somewhere like that.