Brief Summary Of John Stuart Mill's Argument

In the chapter John Stuart Mill provides an argument that utilitarianism should answer before it can be valid. One of those criteria is happiness and in fact the only one, and in order to prove this, one must prove that happiness is the only thing people desire. Mill then goes on in an attempt to prove this and takes into account many arguments, but then disregards them by saying the ultimate end goal of those arguments is happiness, or at least the root of them were, and it makes sense. It makes sense that everyone’s ultimate goal in life, the thing that drives them forward is happiness. In fact, there are people who cannot find happiness in life that may decide they are not willing to live. Utilitarianism states that an action is right if the greatest happiness for the greatest number of people is maximized.
This example has been used before, but let us take it a step further, what if the person to be killed, was unhappy with their life and had given up on life. Even in this situation it still seems wrong to kill them. To me, Mill’s answer that happiness is the only desire is vague in its attempt to explain why utilitarianism is true. Happiness delves much deeper than the happiness of one’s self. Why is it, even when someone is happy, another person’s unhappiness can take it away. To provide an example, a parent’s happiness can often be a reflection of their own children’s happiness. Although, this isn’t the case for everyone, there are many people that have and may now be going throughout their life happy while seeing others unhappy or even by taking away happiness from