Life could perhaps also just use a computer, and exists entirely as software. The computer could be implemented with something other than atoms, perhaps. Maybe some particles shooting among the neutrons of a white dwarf star or something. (My point here is that life doesn't have to be chemical, based on the elements and compounds.)

However, for chemical life, there are indeed only a few ways. We understand the elements very well and the kinds of combinations they express: what kinds of chemistry are possible for all the elements.

Only a few elements exhibit the expressive variety of molecular forms that plausibly support the complex structures that are arguably needed for the chemical representation of life.