t has two sources.

first, the use of "formal language" in logic and philosophy of language in the work of Gottlob Frege in the late 19c/early 20c. Frege was clear that the "formal languages" he developed were not like human languages, but they have nevertheless sometimes been construed this way (although not usually by philosophers and logicians).

second, from work in the late 1940s and early 1950s by Grace Hopper, others at the Navy, and some in academia (particularly Harvard and MIT) to make what were then called "computer codes" and basically required high-level knowledge of mathematics, easier to use, and also compilers to automatically turn these new forms (including well-known PLs like COBOL and FORTRAN) into machine code. They called these "programming languages" in part to distinguish them from "computer codes" and because they used elements of natural language in their construction. almost immediately, people started construing these constructions as some artificial meta-category called "language," despite this being an incredibly contentious (and basically entirely inaccurate) way of construing things. Chomsky's 1950s papers on context-free grammars did not help things.

Have some work-in-progress on this topic as it's a particular pet peeve of mine, but at this point pretty far back on the backburner (if anyone wants to contribute please drop me a line, as I'm very interested in making it a group project).

David