There are many reasons why people would support assisted suicide. Let me give you a few possible reasons.
First, they may argue that assisted suicide is the most merciful thing to do in view of suffering. For example, say you have a friend who is about to die and is suffering tremendously and he or she asks you to help take his life, would you? It is not an easy answer.
Second, there is also the issue of freewill. Some people believe that people have the absolute right to make decisions, even decisions over life and death. From this philosophical point, they may help.
Finally, there might be economic motives involved. I hate to say this, but sometimes people may help, because they do not want to be burdened by the potential financial strain and other potential hardships.
One of the primary reasons there is support for assisted suicide lies in the notions of compassion and dignity. The case for assisted suicide is that if a person is in interminable pain and is in a tremendous amount of suffering, allowing them to die is a merciful approach to easing their pain. The belief is that it is inhumane to continue or prolong their pain if one is in the position of power to alleviate it. This sense of compassion, it is argued, allows a sense of dignity to be restored to the patient. For those who are immersed in an interminable condition, their dignity and power is stripped from them. They are not in control, their body under siege, with the only companion constant pain and imminent death. The belief is that in allowing the individual in such a condition the right to end their own life, they retain dignity of spirit and character and exert power over a condition that has rendered them powerless. The Supreme Court has ruled that people do not have a constitutional right to assisted suicide. This has outraged supporters of assisted suicide, as they believe the court has little or no jurisdiction to tell a person they must live, when they choose no longer to do so.
To answer this question, I would like to apply the cardinal management principle that the authority to break a modify a rule lies with one who has made it or someone superior to him otherwise it results in total anarchy.
Assisted or otherwise, suicide is taking life. Those who believe in God, The Creator who gave life, know that only He has the authority to take life. This right lies with Him and no one else.
So the people who support assisted suicide do so because they do not believe in the authority of God and can find any reason for that as given in ANSWER 1.