A simple “We don't know” is often the best answer for some questions, perhaps even for the title question, suggested by this issue's editors of Current Opinion in Chemical Biology. Because we have direct knowledge of life only on Earth, and as known life on Earth descended from a single ancestor, we have only one data point from which to extrapolate statements about the chemistry of life generally. Until life is encountered elsewhere, or aliens contact us, we will not have an independent second dataset. We may not even then, if the alien life itself shares an ancestor with life on Earth.
We can, of course, conceive of alternative chemical solutions to specific challenges presented to living systems. We can then test their plausibility by synthesizing, in the laboratory, unnatural organic molecules that represent the alternatives, and seeing if they behave suitably. Some of these alternatives come from simple “Why?” or “Why not?” questions. For example: why are 20 standard amino acids used in Terran proteins? Experiments with unnatural amino acids (using the natural ribosome to incorporate them into proteins) have expanded the amino acid repertoire of proteins. These experiments find no reason to exclude alternative sets of amino acids from hypothetical proteins in hypothetical alien life forms.
Similar questions can be asked about DNA. For example, why does Terran genetics use ribose and deoxyribose? Why not glycerol, a hexose or a tetrose? Again, synthetic chemists have made DNA analogs using each, and studied their behavior.