This is a classic causation/correlation error. They establish that there is a correlation between countries that have banned tobacco advertisements and a reduction in smokers and especially in first-time smokers. Be careful not to input your assumptions by thinking "Oh yeah, must have been the lack of ads that caused the reduction", this is the mistake the author of the passage makes. All that was done is that the author established a correlation. The author then concluded that there is a causal effect between tobacco ads and smoking.
The author failed to consider several possibilities, which is the case with all correlation/causation errors.
If we have a correlation between A and B, and follow this by concluding that A causes B. Then we did not consider the following:
Perhaps B caused A. Perhaps X caused both A and B. Perhaps there is no causation at all between the two and it just happened to occur at the same time.
And this is exactly what answer choice C is doing. It is weakening the argument by pointing out the error that the author did not consider that perhaps X causes both A and B. In this scenario, perhaps the attitude towards smoking caused the decrease in smoking and first-time smokers as well as the ban on tobacco advertising.
I hope this helps. Please let me know if you have any other questions!