I couldn't find this exact question, though obviously there are many related questions around using contractions.
I write academic work in a field where contractions are accepted but rare, and no serious reviewer or copyeditor rejects or demands rewrites of a work for using contractions. But, there certainly exist purists who claim that all contractions (well, the ones with apostrophes in them, anyway) are inappropriate in our field and all formal works. I clearly disagree with this attitude, but this isn't a question about who's right in this age-old debate.
What I'm trying to discover, and have thus far failed to, is where this proscription actually comes from. Who first suggested that contractions are inappropriate in formal writing? The proscription isn't in Strunk & White, it's not in APA, it's not in MLA, it's not in CMS, and it's not in the Oxford Style Guide. Certainly any of them'll tell you to be thoughtful about when to use contractions, for instance not using the awkward contraction “them'll”, and surrounding commentary sometimes repeats the banishment as essentially a well-known rule, but the question remains: who's to blame? Is it even known? Is it something that used to be in style guides but was removed in later revisions? Is it something from style guides that are now obsolete?
To me, it seems like someone decided that “stilted” and “formal” are synonyms, and we've been repeating their bad advice for two centuries. I'd like to know who that someone is.