Hi there!

The first thing I'd say is that you draw a sharp distinction between a theistic and a naturalistic explanation that would have been alien to most thinkers prior to the quite recent past. Take someone from the scientific revolution era… Descartes, say. Descartes recognizes a distinction between religious argument and philosophical argument, but he’d be inclined to say that while you must take somethings on the authority of scripture (or faith, or tradition, or what have you) that philosophy also teaches us things about God. So, for example, Descartes is famous for his work on the laws of motion, which are still often cited as being one of the most important sources for our modern conception of the laws of nature. But to Descartes, these laws are ultimately explained via what we can know about the nature of God:

God’s perfection involves not only his being immutable in himself, but also his operating in a manner that is always utterly constant and immutable… and it follows from what we have said that this fact alone makes it most reasonable to think that God likewise always preserves the same quantity of motion in matter... From God’s immutability we can also know certain rules or laws of nature (AT 8:61-62)

The upshot here is that Descartes we knew via reason that God existed and had certain properties, largely because he thought the ontological argument was sound. Since this doesn’t appeal to faith or the tradition or whatever, he feels totally justified in helping himself the that notion of God in his physics.

Now, to get back to Aristotle. He, like Descartes, would have resisted any hard and fast distinction between natural explanation and theistic explanation. The unmoved mover is part of the natural world, for one thing, and for another we know of the existence of the prime mover via reasoning about the world. We know the prime mover exists by reasoning about motion, as he says in the Physics:

The motion of all things that are in motion is either natural or unnatural and violent… all things that are in motion must be moved by something… Now we say that the thing is moved both by the last and by the first of the movers, but more strictly by the first, since the first moves the last, whereas the last does not move the first. If then everything that is in motion must be moved by something, and by something either moved by something else or not, and in the former case there must be some first mover that is not itself moved by anything else, while in the case of the first mover being of this kind there is no need of another (for it is impossible that there should be an infinite series of movers, each of which is itself moved by something else, since in an infinite series there is no first term) -- if then everything that is in motion is moved by something, and the first mover is moved but not by anything else, it must be moved by itself. (255b31-256a20)

Aristotle’s thought here is that things always move for some reason, namely because they are moved by something. This is a completely reasonable thought: Imagine the response you’d get from a scientist if you suggested the things in their experiment moved for no reason at all! Aristotle then argues that this shows that there must be some prime mover, since obviously if we posit an infinite series of movers there wouldn’t be anything to get the motion started.

Now, thus far we don’t seem to have anything approaching theism. But Aristotle then goes on to show that the prime mover must have various attributes, such as that “the first mover must be without parts and without magnitude” (266a10). This of course starts sounding more like something theistic; it is common enough to suppose God to be immaterial and simple, after all. Elsewhere in the corpus we find Aristotle arguing that the prime mover must be “substances without matter; for they must be eternal… Therefore they must be actuality” (1071b20-21). Again, we get divine-sounding claims, that the prime mover is eternal and purely, perfectly actual. But what really makes the prime mover clearly divine is that, well, Aristotle explicitly links the prime mover with the divine in Metaphysics 8 and 9. This is clear enough from the fact that Aristotle there speaks of the prime mover in comparison to the Gods, as divine, and as a thing that thinks. So all and all, we do get that the prime mover is certainly a divine being by Aristotle’s lights. Though, again, one that we come to know not by consulting some canonical, authoritative text or by supernatural revelation, but by striving to understand the world around us in a rational way.

Now, I actually would posit that your professor would agree with all this. He or she was probably trying to stress that Aristotle means to be giving a natural explanation justified by observation and reason rather than by faith. Another good reason to speak as they did is to drive home the distinction between Aristotle’s prime mover and the Judeo-Christian concept of God we are all walking around with, since whatever else the prime mover is, it certainly isn’t that.