There is no objective basis for morality.

I have accepted your challenge, as I know I can prove that it is immoral to kill another person. You make a good argument, but the logic will soon fall apart as I demonstrate that people should not kill other people. First, if (in the scenario you presented) the person the islander killed was indeed not presenting any harm, then there was no reason to kill him, you gained absolutely nothing. While it is true that a sense of morality sometimes stems from person beliefs and therefore becomes subjective, it is not true that murder falls into that category. This is because if you gain nothing from killing someone, and that person loses everything, it is a net loss. Objectively, a net loss is bad. Actions should not be taken by any individual that do not benefit himself, and certainly not ones that not only present no self-gain but also present the loss of a life. Your rebuttal may include something like "he could not have lived on this island without consuming my resources, and therefore would have died anyway". However, I must point out that killing someone who does not present and actual danger to you that is equivalent to murder is irrational and unjust. If you believe that he would have consumed your limited resources and therefore degraded your quality of life, it is possible to morally present him with equivalent harm (e.g. protecting your island and it's resources from his grasp) which may result in him dying but would be moral. It would be moral even if you knew he would surely die because you are only taking actions to defend your property and not actively kill him, he would only die as a result of being incompetent. In other instances, where killing someone is your only means of surviving, it is not immoral. For example, if someone invades your home and you believe he presents a lethal threat to your well being, you can morally kill him. However, in instances where your life is not being threatened it is immoral to kill because there is no point in it and objectively (as I said before) it is a net loss. Another instance is armed robbery. If you murder someone to take their possessions you may say it is a net gain if you get enough money. It is not. This is because you cannot valuate a human life in the same way you would valuate an inanimate object of an animal's life. A human life is regarded as self-owned. You can valuate a bottle of soda or a cow based on characteristics such as demand, supply, labor cost, market competition, etc. However, we can agree (hopefully) that man does not live for the sake of his neighbor. It seems you must support that ideal. So, assuming you do, how do you use such characteristics as demand, supply, labor cost, market competition, etc. to determine the value of human life? The answer is simple: you can't. So if you cannot prove the worth of a human life, you cannot justify trading it for any object (material or not). It must be assumed that, objectively, human life is of the most importance. Without this idea, the human race could never grow and innovate as quick as it has (or at all). Instead, we would act like animals, killing each other for territory and access to limited natural resources; instead, we have accepted the previous idea of morality, and thus have engaged in civilized competition for the positive creation of wealth and the efficient exploitation of natural resources. I hope you can present an argument that explains why you think it is alright to murder another human being, and why you think it is a net gain for you, your friends, or anybody at all.