> 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.