It's all because because of an archaic definition.
Here's one of the definitions Noah Webster gave for copy in 1828:
An original work; the autograph; the archetype. Hence, that which is to be imitated in writing or printing. Let the child write according to the copy. The copy is in the hands of the printer. Hence, a pattern or example for imitation. His virtues are an excellent copy for imitation.To us, the phrase "original copy" is an oxymoron. To our forebears it was redundant.
This definition had fallen out of use by the mid nineteenth century, except among printers and newspapermen.
Some time around 1870, the man who wrote the advertisements began to be called the copy writer, to distinguish his work from that of the news writer.
Translated into Modernese, copywriter and copywriting become originalwriter and originalwriting.
Another archaic definition of copy: Abundance, or wealth.