Well, there are two reasons. The first is that *our* type of life is carbon-based, so we have the most knowledge of that kind -- also we serve as proof that carbaon-based life *is* indeed possible, we're not so certain about any other types.
The second is that carbon is an extremely "versatile" element, capable of combining is so many ways that practically countless different kinds of molecules can be formed from it (thus producing a vast array of molecules that produce the sort of molecular complexity that can make life processes possible. Also carbon makes for molecules that are neither too tightly nor too loosely bound -- molecules that are too tight won't interact easily, and molecules that are too loose will disintegrate spontaneously too often. As far as we know no other element has properties as ideal for life-suitable compounds, although silicon seems to be a decent (although not ideal) second place, and silicon-based life seems to be at least a possibility.
However, even looking at only *chemical* based life may be too restrictive. For all we know life may be possible based on nuclear processes under the right conditions (like inside the sun), or who knows what else.