How can I introduce a fourth reason after having stated that there are three main reasons? In an academic paper, I have written "There are three main arguments for why X is not Z."

I have then discussed them like this:


  "First, ....​ (of medium length)
  The second argument is that ... (a bit long)
  The third and most important argument is that ... (longer)"​ **


** I did not simply use "First,... Second,... Third..." because there is some distance between the arguments. For example, the second argument is two pages long. I think writing "The third and most important argument ..." reminds the reader what these arguments are for.



​
Now I have realized that I have to make one more argument. And I want to start with "A fourth argument is that ..." after the third one.

Is it a problem that I stated in the beginning that I will give "three main arguments", but I give four? I don't want to say "four main arguments". 

The three main arguments are widely discussed by experts in the field. The fourth argument is something that has only been pointed out (in two lines) by one author. The Thing is, my supervisor likes this fourth argument and thinks I should include it in my paper. That is why I want to mention it. I don't want to say that it is trivial because it can become important sometime in the future - just that it is not a main argument (or widely discussed) for why X is not Z.

What is the best way to introduce the fourth argument after the third while maintaining that the first three are the main arguments?
I did not simply use "First,... Second,... Third..." because there is some distance between the arguments. 


I suggest that you open with: 

There are three main arguments for why X is not Z: A, B, and C. 

Then, rather than First, ....​ (of medium length)
The second argument is that ... (a bit long)
The third and most important argument is that ... (longer), you can use A, B, and C as section/subsection/paragraph headers.


  Now I have realized that I have to make one more argument. And I want to start with "A fourth argument is that ..." after the third one. Is it a problem that I stated in the beginning that I will give "three main arguments" but I give four? I don't want to say "four main arguments". 


That's a problem, just write There are four main arguments for why X is not Z: A, B, C, and D. and use D as a heading. 


  The three main arguments are widely discussed by experts in the field. The fourth argument is something that has only been pointed out (in two lines) by one author. 


You could revise the opening as:

The literature agrees upon three arguments for why X is not Z: A, B, and C [1,2,3,4,5].

And follow that with:

A fourth argument has also been identified: D [6].