When searching for signs of extra-terrestrial life, the key primary challenge as of now seems to be searching for signs of water on other planets. Presumably, this is because on Earth, water is necessary for all life.
However, what if we discovered organisms on another planet which exhibited respiration, reproduction, or even social interaction, in a similar way life on Earth does, but which has evolved without the need for water? We would still consider this a form of "life", and certainly it would be a worthy find.
It seems perfectly possible that other substances besides water could come together to create something that we would perceive as "life". This could either be through other substances which contain Hydrogen and Oxyen, or because there are other elements (including elements not yet discovered) which could combine in a way that appears to create "life", just from a different direction.
"Life", in a broad sense -- and certainly in the sense that extra-terrestrial scientists would be interested in -- is just a series of chemical reactions which happen to have allowed for reproduction / respiration etc.; but this has no relation to the existence of water. In fact, given the vastness of the universe, the vastness of the number of potential new chemicals and new chemical reactions out there, and the relative insignificance of Earth and its beloved water amongst all of this, it seems unlikely that if there is extra-terrestrial life, it would be water-based.
So why, then, do we focus so much of our efforts on searching for extra-terrestrial water? Is it because it's a good starting point and we don't know what else to look for? Or is it because I am wrong in thinking that other forms of "life" could have evolved without water?
(This question relates only to the search for extra-terrestrial life, not for other uses of extra-terrestrial water, such as colonisation.)