The essential problem with individual morality is that in some individuals, the good morality that they develop for themselves can be completely unlike that of anyone else, and in that, it can be what most others would not consider morally good. This is the reason that society has the responsibility of passing on general morality. Often times, people are not the slightest bit concerned with morality, in which case the idea of good and bad is pointless. These are the people whom society fails.
It seems more like the people have failed society. There is no way an entire society can pass on morals to individuals, as the society is composed of individuals. It is the responsibility of each individual in society to agree with several other individuals upon key moral values, which is well facilitated by our language capabilities and ability to recognize patterns. If a new behavior or change in mindset chaotically evolves in an individual, it either propagates and spreads like an infection through the populace, or is quashed promptly by the "homeostatic thought-immunity system of the human collective," otherwise known as random emotional human whims and massive communication capabilities.