Though Western culture has become invested in a notion of individuality, we remain interested in (and conflicted by) the constraints of roles. Family roles, social roles, and professional roles all still occupy an important place in our culture and in our thinking.
The rules we follow are often governed by the role which we are filling. From the Greek canon, Electra and Orestes were beholden to a certain role that behooved them to revenge their father's murder. In doing this, they were forced to betray another moral code that governed their relationship with their mother.
The moral conflict that grew from this situation is created out of the deep investment that the Greeks made in the importance of formal roles and rules of behavior. We can make the same argument about Oedipus.
In today's world, doctors and attorneys, counselor and teachers, and even parents can face dilemmas that are similarly role related. The rules of a doctor's behavior are tied to his or her role as a physician, yet there are times when the right thing to do medically is not the right thing to do morally, or vice versa.
A parent who becomes aware that a child has committed a crime will experience a conflict that grows from a conflict of roles. As a citizen, the parent should turn in the child. As a parent, the urge will be to protect the child.
Dilemmas such as these are often the subject of contemporary drama, on stage, in literature and on film. While we believe more strongly in individuality today in our culture than the Greeks did in theirs, the notion of roles driving conflict is still strongly present.