The problem is that you remove the final cause and the efficient, or immediate, causes come crashing down. Cause and effect become loose and separate as Hume puts it. Take a different example, one where purposeful human action is only peripheral; the heart. Now if we can say the final cause of the heart, and all it is made up of, is to pump blood around the body. Now we know that this is what it does from observation. We therefore say its final cause is to pump blood around the body, its formal cause is the properties that are required for this like a certain muscular toughness and texture and all the division in ventricles and what have you, and they all express its nature or essence.The nature of a ball is not to be used in a child's game unless you define 'nature' in such a way to allow you to reach said conclusion by including such things as natural in the definition.
The "final cause" is an arbitrary decision to claim that this is what such an object can be used for. But a rubber ball is equally usable to plug up the sphincter of a kinky fetish model. Who defines the "appropriate" final cause? The person trying to make the circular argument vilifying or justifying a certain behavior, that's who. And they do so by reverse engineering their logic from the conclusion to the premises, carefully creating premises that imply their desired conclusion.
Now you might say this is an arbitrary view, though arbitrary is probably the wrong word and mistaken understanding of what is taking place is more correct because you will probably be implying there is no purpose involved, it is all just parts coming together fortuitously with no outside direction. But the challenge of Aristotle, Aquinas and indirectly Hume is that take away the final cause of the heart, to pump blood and the cause and effect become loose and separate; or as Aquinas puts it, if we remove the end of final cause of a cause (an efficient or immediate cause) then there is no reason for one cause to follow another except by chance. In other words if you remove the final cause of those things or efficient causes, that make up the heart, from its DNA upwards, then there is no reason for them to form into a healthy heart and keep the apparent order and purpose they haveand not a piano or a plate of humus. If you were a hardcore Humean you might say so what (at least when arguing, though as the common sense philosopher Thomas Reid quipped of Hume it is hard to take seriously someone who claims to=have such a position and still lives a relatively normal life), but most of us are not and do not think it likely that the orderly and regular progression of cause and effect we experience everyday is all just chance. There are more arguments in favour of the Aristotelian, but I think most people balk at the full implications of causality without final causation when they realise what this means, as Hume did though whether he actually knew the proper Aristotelian position I'm unsure. One important point is that this final cause shouldn't be mistaken for necessarily some sort of conscious, anthropomorphic action. The point is that this can happen with or without conscious involvement depending on what we are talking about.
This doesn't make much sense, to me. If we take natural as according to nature and essence then we still need to find out what the nature or essence of any particular thing is. In Aristotelian-Thomistic perspective we do this by looking to its formal cause or properties and particularly its final cause or end, we see this from observation or induction and rationally analysing these. If it was so obviously circular then Aristotle, the Angelic Doctor and all their commentators would have immediately noticed it. Unless you are just objecting to the assertion things have natures or essences and think this is unproven, although I think the proof for it has basically been given. Well, obviously, I don't think it is too controversial to say we see things in the world that usually seem to have certain properties and that they sometimes share some of these with other things. From there we can investigate to what degree these properties are necessary to them, what is necessary to them and what relationships they have with other things. None of this is circular, though any particular argument you might not find convincing.When you have to "relate" that which you wish to call "natural" or "unnatural" back to your definition of "natural" or "unnatural", you cannot possibly have employed anything otehr than circular logic.
Why? Because as any student of logic knows, conclusions follow from the premises. You, however, have been demonstrating the complete opposite of a logical progression, and your language choices demonstrate that perfectly. If the argument must be "related back" it certainly does not follow, at least on it's own merits.
Since the conclusions are what must be "related back" to the premises (and not by virtue of a premise), we can clearly see that the arguments involved are invalid ones.
I think one problem is that you are confusing what is deductive and inductive. We reason that things have natures based upon a first look at our plane of existence, we reason in general how to deduce what we can about their natures and then, when it comes to specific things we use our deduced method to reason based on what we see through induction or observation. This is generally the Peripatetic way; the Platonic way is to intellectually, not discursively but through direct noetic vision, grasp the intelligible essence of a thing, but as such a position relies on an appreciation of the power of the intellect far above what moderns in general will allow, I have ignored the Platonic viewpoint in general in this discussion.