While I was never obliged to drink turpentine as a child, I was haunted with the idea a few times. We had access to doctors. My parents, however, were given a few drops occasionally during their childhoods to ward off intestinal worms and other parasites. See, pines trees developed sap that kills parasites, and turpentine is distilled pine resin. Turpentine is good for thinning paint, repelling water, and as fuel for lamps. That doesn't mean it's safe to ingest, but it has a long history as a medicine.
Viewed in context, it’s easier to understand why doctors once used it as medicine. Pine tar, another related product, is still a useful medicine ingredient for rashes and skin problems, while turpentine oil, which was also considered good for lung health, is still an ingredient in Vick’s Vapor-Rub. (Although it’s listed as an inactive ingredient.) Turpentine is antiseptic, too, and the terrible taste and harsh effects could have been interpreted as signs that it was working. “King of the [medicines] was turpentine, a product of the tidewater pine forests,” Kentucky historian Thomas D. Clark wrote. “Turpentine had three important medical requisites: It smelled loud, tasted bad, and burned like the woods on fire.” It also had the strange side effect of making urine smell like violets.