Religious people like to argue that human morality is dependent upon the Christian worldview to make sense. They use this argument as a support for the necessity of their God. They like to argue that without God as a basis, there is no objective morality. I tend to agree that there is no objective morality. Instead, I refer to a shared subjective morality. Our humanness is what determines and leads to this shared subjectivity. I've found that the following explanation, based upon scientific knowledge from biology, sociology, neurology and psychology, usually works to refute the Christian claim, and to establish a coherent moral picture, without having to appeal to any deity or religion.
A humanist model of morality owes nothing necessarily to Christianity. When you observe other animals in nature, you find that animals which evolved to be dependent upon other animals for mutual survival, i.e. social animals, also evolved to allow for a predisposition to remain a more or less cohesive whole. This is generally expressed as a fuller spectrum (positive as well as negative) of emotionality. Depending upon the relative cognitive sophistication of a given species, we can see a more complex set of proto-morals developed. The most intelligent and self-aware organisms besides humans really illustrate this very well- dolphins and other primates, especially. The organisms that developed to be solitary, usually lone territorial predators, do not normally exhibit these predispositions. Compare our two most common pets, cats and dogs. Dogs are evolutionarily social animals. Cats are not. Both have been domesticated. Both are loved by their owners. But study after study shows that dogs demonstrate an emotional connection that cats don't, that they are not wired to have.
The surest way to overcome a prejudiced hatred of a race, gender, or any difference, is to have the hater work and live with the hated. This engenders a sense of identification with one another, and thus the extension of empathy. This shows that the basis of morality is shared emotionality, aka empathy. As a species becomes more cognitively sophisticated and self-aware, the more developed and rich the ability to express and presumably to experience empathy. Nietzsche observed that the etymology of words referring to morality are quite telling of their development. For example, the word kind refers both to a group bearing some unifying similarity, as well as to treat others benignly. This reflects the strongly evidenced fact that empathy is only extended toward those with whom we identify, to the extent with which we identify with them. The surest way to overcome a prejudiced hatred of a race, gender, or any difference, is to have the hater work and live with the hated. This engenders a sense of identification with one another, and thus the extension of empathy.
The mental disorder antisocial personality disorder (formerly referred to as psychopathy and sociopathy) is characterized by the lack or blunting of positive emotions, both self-directed and other-directed (empathy). This illness generally is associated with trauma and/or negligence in early childhood, often before age two. A child raised in a fairly normal setting and manner will develop a healthy sense of empathy. It's the normal and usual path of human development.
Another part of this is social mores implicitly introduced and enforced by the person's social milieu. This is also the result of the social animal path of evolution. It allows us all to get along.
In addition to these, we have created pragmatic rules (laws) as a society which cover other behaviors that would threaten our ability to exist in larger groups.
The first part (empathy) is generally universal along humanity. The second two parts are more heterogeneous, depending upon culture, geographic location, and environment. All of these are dependent upon and emerge from our evolutionary path of development. This is the source of our subjectively shared sense of and practice of morality. From this basis, this universally shared subjectivity, arises the less widely shared variations. An objective morality is not needed and is not supported by the evidence. Our sameness and our difference come from our humanness. This is the basis of humanism. Religions need not apply.