To believe that you are more important than someone else without any objective evidence makes no sense. This is likely derived from the easy yet illogical belief that the fact that “you are yourself” means that you are therefore the most important thing to you. The only context in which this assumption is valid is for animals that live alone and have to survive, which does not reflect humanity at all because we have transcended that. A clear counter example to this extreme use of subjectivity is giving your life for someone else. People who believe that selfishness is good would call self sacrifice illogical, because of their easy life philosophy which means that they avoid making hard decisions and having to deal with the moral implications of them.
Most people will want to live instead of letting someone else live if forced to choose, but that is not what parents do with their children, or what activists and revolutionaries do for freedom and justice, it is what your subconscious instinct tells you do to. In some cases your subconscious would be right, but when it comes to choosing between two lives or any two extremely important things, your subconscious cannot make an informed and unbiased decision like your consciousness and morality can because your instinct is arbitrarily pre-programmed. To let your subconscious choose for you is to avoid making the choice yourself, and to avoid the moral consequences of it.
This situation is an extreme which no one should ever have to be in. No human life should be considered more important than another. In some cases when you cannot save both people, one must make a utilitarian objective decision the best they can about who to save. If you know one of the people, or even worse if you love one of the people, you will likely want to save them instead. This argument is valid, but not sufficient, because there might be people who love the other person, and the only difference then between the two people is one you have in your mind. The fact that you are making this decision though does not warrant your opinions of the people deciding who will live. One cannot say that those that they love are more important and deserve to live more than others, because everyone has that same argument for different people. These arguments are subjective, and there is no way to choose who is correct when everyone says their loved ones are more important. For you to let your feelings about the person alone decide who will live is therefore abusing your power.
Instead, the best you can do, although this is still not good, is to try to decide who of the two people will live a life that results in more good. This is not an easy choice, nor is there a known way to do this objectively. You have to predict which is the person who will make others more happy, or make more people happy, or make more people happier, the person who will help more people, the person whose will make fewer people sad. There is a seemingly infinite amount of variables to consider, which may result in you knowing that the person whose life is more important than yours, or more important than the life of the person you love. To ignore this is to ignore your morality and simply do what will make you feel better through ignoring the truth.
Such a situation should never have to happen to anyone. This is why we must not allow these situations to happen