Atheist VS Naturalist - the latter sounds more appealing to me...

[Belacqua]

But it would be natural just abnormal

According to the definition I'm using, it would be supernatural. I've explained why.

Why do you say that a frog doing what a frog can't do would be natural?

 and certainly an outlier but being an outlier does not make something unnatural.

Outliers, as I understand it, are possible but rare. They are still within the bounds of science, in that they can be tested through repeatable empirical methods. 

You've introduced a new term here: unnatural. What do you mean by this?

 AGAIN I'll ask why should we give credence to an idea such as supernatural without any supporting evidence?

I'm not saying you should believe in the supernatural. 

I'm saying that when you talk about "any supporting evidence" you are begging the question, since the evidence you accept is the kind that doesn't address things which are non-repeatable and non-empirical.