On False Distinction

So one of my professors tells me that he does not understand the materialist/ supernaturalist distinction. Now of course, he does actually understand it and he really just thinks it is bogus or at best trivial and meaningless. But his "rub you the wrong way" method of communicating does not automatically determine the truth value of his arguments. They still could be right. He tells me that the term supernatural is like the term fuzzy- only with more baggage. That is to say a supernatural being (such as an angel) is like a fuzzy animal (such as a kitten). So his question seems to be- what does fuzzy really tell you about the cat? In the same way- what does supernatural really tell you about the angel? He told me that the distinction may be largely to blame for the belief that some people have that science is somehow anti-religion, or anti-God (or gods). Now the challenge he put to me is to define supernatural in some sort of meaningful way. He did not seem taken with my suggestion that it was both significant and meaningful for supernatural to be a statement of our ignorance. Angels are not subject to the "laws of nature" I said- they may be subject to laws- but we do not know what they are. He asks me then, is anything not subject to the laws of nature then appropriately called supernatural? What about things before the big bang? Are they supernatural?
So I am thinking about it, but what things before the big bang? My problem is that I still do not quite grasp the fuzzy animal analogy. I mean I see what the analogy is saying- but I just find it easy to see what supernatural is saying- what it means. Now, of course, he wants a philosophical definition- which is a bit of work- so this will be continued later, but I think that when God disrupts the natural laws of the universe to perform a miracle that it makes perfect sense to call that a supernatural event. So what he wants to know (basically) is why anyone would insist on calling the ressurection of Jesus Christ a supernatural event. I think that is a valid question for him to ask. The answer will take as long or as short as it takes to think about. I suspect a significant amount of meditation will be required. May the Lord grant me wisdom beyond my years.