The fundamental difference between comprise and compose has to do with the whole versus the parts of any object or concept. Let’s take a closer look at the definitions to put this in context: comprise is a verb that means “to include or contain” or “to consist of” as in The pie comprises 8 slices. Compose means “to be or constitute a part of element of” or “to make up or form the basis of,” as in Eight slices compose the pie. The key rule to remember is that the whole comprises the elements or parts, and the elements or parts compose the whole.
Their slippery meanings and similar sounds have likely contributed to the rise of “comprised of.” The argument against this phrase is rooted in the definitions outlined above. If we hold comprise strictly to the definition of “to include” or “to consist of,” then “comprised of” sounds awkward: The pie is included of 8 pieces sounds nonsensical, and, by that rule, so too does The pie is comprised of 8 pieces.