When did quitting smoking become a thing?

The song “Smoke, Smoke, Smoke That Cigarette” at least shows that it was recognized as an addiction in the 1940s.

In Rudyard Kipling’s Captains Courageous, published in 1897, there’s a scene where a spoiled rich kid, rescued by a fishing schooner after falling overboard, has his first interview with the schooner’s captain.

At one point he reaches in a pocket for a wad of cash, but pulls out only a soggy pack of cigarettes. The captain says “Not lawful currency and bad for the lungs - heave 'em overboard and try again.”

Something to keep in mind is that although cigarette ads had doctors in them saying that smoking was safe they were there to combat public perception that tobacco was harmful. If nobody thinks your product is unsafe why put the idea that it might be unsafe in peoples minds. So as soon as you see doctors in tobacco ads you know that there was a strong anti-tobacco movement.