Morality is constructed rationally when it takes in as much of the complete picture as possible. It is the art of observing and understanding the cause and effect relationships in these approximate, experiential systems.
Edit: Let's address the issue of caring about people. Some propose it isn't logical. If it were true that individuals do not rely on others for survival, then I could understand that argument. Of course caring about people is logical if you want to have a support system to survive in the world. Think about when you grow old - the person who was caring and formed a support network is going to survive those years of increasing feebleness with much more strength and grace than the person who has ostracized everyone. This is exactly what I am talking about when I say it requires viewing the big picture played out over time to understand all the cause and effect relationships of behaviors. To come closer to home, you would not presently exist if your mother or guardian didn't care about you. The fact that humans have vulnerable offspring is why we developed the instinct to care. To go against that natural design is both arbitrary and irrational.
I'll look back over the thread in search of someone who has made some kind of argument demonstrating that it is more logical to not care - besides merely stating a supposed correlation. Edit: Maybe we should define morality. My premise is that morality is not defined by social constructs like religion. That is one manifestation of it, but those constructs can become arbitrary and then distort the natural course and in this way become irrational. When I use the word, "morality", it refers to any ideal that supposes having a constructive outcome for the group and so includes the ideals of caring, responsibility, honesty and other such things depending on the context.