Famine, Affluence, and Morality

In Peter Singer's "Famine, Affluence, and Morality", he argues that the way people in relative affluent countries react to a situation like that in Bengal cannot be justified. His reason for saying this is due to his belief in his principle "if it is in our power to prevent something bad from happening, without sacrificing anything of comparable moral importance, we ought, morally to do it". I disagree with his point of view and I will provide explanations as well as bring in my own arguments to show why I refuse to accept his said conclusion.
Singer begins with the assumption that suffering and death from lack of food, shelter and medical care are bad. Therefore, according to his principle, we must to our best prevent situations such as that in Bengal where people die from lack of food, shelter and medical care, from happening (by donating money), without sacrificing anything comparably important. We could deny this assumption but in doing so, we would not be honest to ourselves. Assuming the Principle of Universalizability, he claims that it makes no moral difference whether the person I can help is a neighbour's child ten yards away or a Bengali stranger who is ten thousand yards away. I will challenge this assumption by modifying his example: There are two people drowning in a pool, one is your cousin and the other is a stranger. You will almost instinctively swim towards your drowning cousin because you will feel more morally obliged to save him than to save stranger. What if the two people drowning are both strangers, one is an old lady and the other is a young man? Naturally, you will feel more morally obliged to save the old lady because she appears weaker as compared to the healthy young man. This goes to show that there will always be a moral difference in choosing who to help. Human nature is such that people will tend to be bias towards the person who gives them a greater/ better impression. No two people will give a third person the same impression