Because I don't understand the quote: "The Stile of this Confederacy shall be the United States of America." I don't understand what a stile has to do with anything, or why they'd describe themselves that way? I don't get it.
I have no idea but I think it refers to the style and not the structure. The newly formed nation was the stepping stones to freedom, something that Europe did not have at that time, especially in religious freedoms.
Standardized spelling wasn't always such a big thing. No less a luminary than Noah Webster though it should be "stile" rather than "style".
"Style" would make a bit more sense here, but its still an awkward quote, unless I'm missing some context.
"To style" in the sense of "to name" is a long-established usage. I still occasionally see it in the form "self-styled".