I just realized something that I do not understand, which is kind of embarassing since I have been learning things that are built on this for the past 2 years without ever actually understanding it.
An enzyme is nothing more than a catalyst, and any catalyst increases the rates of the forward and reverse reactions proportionally (i.e. enzymes do not alter the equilibria of the reactions they catalyze). So how can there be kinases and phosphatases that catalyze reactions that are reverses of eachother? Wouldn't a kinase dephosphorylate its substrate just as much as it phosphorylates it, and if both a kinase and a phosphatase act by reducting the activation energy of the same reaction, then shouldn't a kinase and a phosphatase be the exact same?
I have only one idea for an explanation of this as of yet, which is that the product can change conformation (after leaving the enzyme) in such a way that it no longer can act as a substrate for the enzyme. For example, some kinase may phosphorylate its substrate, which may then leave the active site and immediately change conformation so that it can no longer bind the kinase. The phosphatase, however, would bind it and convert it back to the original. This seems like a reasonable explanation to me, but I don't know that it is (1) true and (2) universally applicable, and I don't want to just go on it like it is true without knowing since its such a fundamental part of biochemistry.