I should say from the beginning that I am not advocating for or against Sigmund Freud's theories of how to understand the human mind. I am borrowing his language because it does a good job of this, at least: capturing how we experience the human mind. Freud talked about three aspects of the mind: the id or animal part of the mind with the passions and lower instincts; the ego or our proper selves that we identify with, and the superego as the ethical or moral side. We see the ego as ourselves, the id as the lower part of us that gets us into trouble, and the superego as our consciences. In cartoon terms the person is the ego, the devil whispering in one ear is the id, and the angel whispering in the other ear is the superego. The picture of an angel whispering in one ear while a devil whispers in the other has become a commonplace in our culture because it captures something of the feel and experience of the struggles we all have at times. Freud pictured stages of psychological development in which the person, as he matured, learned to tame the animal-like id with the help of the superego. Healthy human development would result in the ego no longer being enslaved by the wild and powerful impulses of the id.
The superego, in one sense, consists of the expectations of the society or culture. These expectations inform our consciences. In some sense, our thoughts about society's expectations and religion's expectations form our consciences or superegos. Again, regardless of whether you are a fan of Freud or an outspoken critic, he gives us a language to use for discussing how the conscience forms and how cultural expectations shape an individual's ethical reasoning.
So what happens when cultural expectations for ethical behavior are largely removed? What happens when a number of leading voices say that the ideas of "right" and "wrong" are meaningless or even destructive? What happens when prevailing voices say that morality is solely a private matter? In terms of our inner struggles, it means that the person can no longer enlist the help of the culture in taming his lower instincts. It means that the person develops a less-controlled animal side than would have developed otherwise. It leads to a stunted conscience. It leads to a culture where each individual person has not developed as much as she would have in a culture that had higher expectations. It leads to more people being enslaved by their animal natures, unable to muster enough resources to break free or gain self-control.
When morality is solely a private matter, many of the resources for private morality are lost. And as cultural expectations become lower, as each person's conscience develops less than would have happened otherwise, the entire culture begins to see the effects of our untamed lower instincts.