It’s partly due to the makeup of Carbon. It tends to be a particularly abundant element. The way matter is created, it goes through steps on the Periodic Table. I.e., the larger the element is, the longer it takes to make and the rarer it is. It also has to do with it’s reactivity when an element, and it’s lack of reactivity once it’s bound into a molecule. It’s also particularly life-sustaining and stable as compared to nearby elements — which are the other likely candidates to supporting life.
That isn’t to say it’s not possible, but that Carbon is most definitely the most likely, so why bother looking for a needle, when you want to find the hay?