Aside from the point others have made that carbon based chemistry is a likely candidate for life, there is another factor I think:
We already know that carbon based can exist and we know what it looks like. Since our means for searching for life in the rest of the universe are still very limited, it is best to focus on what we know, instead of searching for a different form of life of which we
* don't know what it looks like
* don't know whether it can exist in the first place
I think the field is potentially wide even within carbon chemistry. Genetics (which seems to have a single origin) could feasibly exist as a completely different yet still carbin-centric "implementation."
We already know that carbon based can exist and we know what it looks like. Since our means for searching for life in the rest of the universe are still very limited, it is best to focus on what we know, instead of searching for a different form of life of which we
* don't know what it looks like
* don't know whether it can exist in the first place