Because the "whole" is in most cases the sum of its "parts." Therefore, to describe and understand a mixture, chemically, it is logical to separate it into its smallest constituents (molecules).
Suppose we drill a hole deep into the Earth and extract a liquid. Principals of enlightenment tell us to know what makes up this liquid, chemically, so we can better know whether it is a useful liquid or this is something we should never do again.
In many cases, it is not the mixture that is useful to us, but rather one or more of its constituents give the mixture its real utility. By separating a mixture into useful and non-useful constituents (called concentration or speciation), we can avoid a lot of useless work.
Think of how many mixtures in our World contain water. Water is everywhere. If we want to transport a mixture containing water across land, then it is likely more economical to separate the water out, transport the remaining concentrated constituents, then add the water back at destination to recreate the mixture.