The Circularity of Aquinas' Fifth Way

In a discussion with the Quantum Thomist, I made a statement to the effect that the Fifth Way of Aquinas exhibits circular reasoning.  The Fifth Way is one of Thomas Aquinas' five famous arguments for the existence of God.  It is also known as his Teleological Argument, or his Argument From Design.  It is based on the presumption of teleology in nature.  Of course, my claim that this argument is circular is something that Thomists don't like to hear.  Most dedicated Thomists are convinced beyond any doubt that the logic of Thomas Aquinas is beyond reproach.  The impeccable logic of Aquinas is the basis of their Thomistic philosophy and the foundation of their theistic belief.  How can someone like me (who isn't even formally educated in philosophy beyond Phil 101) take issue with such a master of logic and philosophical thought?  I will attempt to explain.