To understand why all compounds are "pure" it is important to first understand what constitutes a substance, as opposed to a mixture, as well as what constitutes a compound.
A substance is one of two forms of matter, the other is a mixture. A substance has a definite and constant composition and may be either an individual element or a compound. By contrast, a mixture is the combination of two substances without a constant composition, since it relies on the person or force which causes the mixture to form to dictate its proportions.
One of two substances, a compound forms when two or more elements bond together either through ionic or covalent bonds. While it is possible to decompose compounds chemically to isolate their individual elements, this process takes a large amount of energy and specialized laboratory equipment.
Therefore a "pure" compound simply indicates that a substance includes two or more elements in a specific ratio, which never varies. As in the example above, a molecule of "pure" water always contains two hydrogen atoms and one oxygen atom (H2O). While many other molecules contain both hydrogen and oxygen, only water contains those elements in that exact 2:1 ratio. And, once combined in that ratio, the elements of hydrogen and oxygen have specific, unique chemical and physical properties that are different from either element on its own or any other combination of those two elements.