Well, assuming the scratch was not there when you bought it then, yes, it is your fault.
No you did not wipe away a protective coating to reveal a scratch that was already there. A) If you were wiping so hard that you think you might removed some sort of coating from the device, then I think you need to use a softer touch and B) if there were a scratch underneath some "coating" you would have probably noticed that regardless.
So the next argument is that the screen is somehow defective since it is supposed to be scratch resistant. Apple never claimed the screen could not be scratched or even that it is "scratch resistant". Obviously they don't want to the screen to scratch easily, but there is a limit to what can be done considering technology and cost.
Even if the screen was designed to be "scratch resistant" to anything but, say, diamond. Since you do not even know how the scratch got there how do you know that it wasn't caused by a diamond?
Bottom line is Apple gave you a product without a scratch, you assumed responsibility for the device and now it has a scratch. Like others have said, maybe you will find a sympathetic ear at Apple, but you can't really fault them for this problem.
Some advice.
I don't know how you store your microfiber cloth, but when you are not cleaning something with it, keep it in something relatively airtight. A zip-lock bag works well.
Blow or brush away any particles on your screen with compressed air or a lens cleaning brush before using the microfiber cloth on the screen. That way you will not grind any particles stuck on the screen into the screen.
If you have a lot of caked-on grime which can not be easily removed with a dry cloth then consider using some lens/screen cleaning fluid with a separate microfiber cloth.
And finally, if you have the apple case (or any case of a similar design) always make sure that if you've been using the case as a stand that you make sure that the inside of the case is clean. The part of the case that rests against the screen is the part that rests against the table surface when used as a stand. If the table has debris on it, some of that will stick to the case and then later may end up against your screen.