It is the idea of doing what you want to do, no matter if it is best or not, no matter if it is right or not. Nobody can tell me what to do with my own body. Now, you might think that is extreme, but it is very common. It's just a short step from that dangerous logic, a logic of autonomy, or radical individualism, to insisting upon the right to take your own life. They are bedfellows.
Suicide is an individual and tragic decision that some people make.
But when we as a society are asked to legitimize voluntary euthanasia, then this becomes a public concern because of the potential abuses and exploitation of the most vulnerable people among us. Legalizing assisted suicide would seriously damage the relationship between doctors and patients. Legally assisted suicide would put pressure on elderly and disabled people to choose death so as not to become a burden on others. Legally assisted suicides would result in irreversible mistakes. Legally assisted suicide would dry up resources for those who want to live out their last days in a hospice or at home under personalized care.