Smoking had been known to be incredibly unhealthy by medical practitioners, and was somewhat known by the general public, for a long time; I would hazard the thought of it being a known fact ever since the late-19th century. The only reason people weren't discouraged publicly was because doctors had too much on their plates and didn't have the data to make completely accurate claims that smoking TOTALLY caused heart disease, lung cancer, etc. Especially since, after WWII, cigarettes were all the rage!

But your question was about why children were discouraged. Honestly, children smoking cigars was a common sight in the 1800s, as they were often selling (yes! as clerks!), harvesting, and being featured in ads about tobacco products. Since they were heavily entrenched in the production of cigars and the like, they smoked them prolifically! After many years of this being common, many people (around the 1900s) started to find this unseemly, but mostly it was just European visitors complaining. Once people complained, though, children and women started smoking less cigars and more paper cigarettes.

Soon enough around this same time, anti-cigarette leagues started popping up and protesting the smoking of cigarettes, and they only appeared because it was common knowledge that women and children smoked cigarettes instead of cigars! People didn't want them to have all the nicotine fun I guess.

So to answer your question, there was a big stigma against nicotine and paper cigarettes, and that's what women and children smoked, so it was frowned upon. But the fact that women and children smoked was bad enough.

Sources: The Consumers Union Report on Licit and Illicit Drugs by Edward Brecher

Cigarette Smoking Behavior in the United States