What you choose to do with your body and your life in a free society is your choice and your choice alone. That does not mean that suicide is a beneficial practice, and there should be counseling services available for anyone considered dying, but they should not be demonized for choosing to take their own life after careful consideration.
Nothing is certain in life except for death. This is a well known fact of life and there is little we can do to stop this progression, if anything. I think this fact makes it obvious that a person does have an inherent right to die. People end their lives prematurely every day.
Human beings have an inherent right to die. Various religions have called suicide a sin and intimidated people into thinking that they will not go to heaven if they chose to end their life. A person that is in chronic pain, emotional, mental or physical, and there is no hope of that improving, they do have the right to end their life.
People have a right to die. The people we are talking about for the purposes of this conversation are those suffering the ravages of age or disease. Who are we to suggest that these poor should must suffer so that our sensibilities aren't offended. It is terrifying to consider, but it is true that sometimes life isn't worth living.
I believe that if someone is suffering from a terminal illness or a terminally compromised mind (permanent dementia for example) and either communicates a desire to die at that time or has a living will in case they are unconscious or their mental faculties make it impossible to make an informed decision then they should be allowed to die.
But if someone is just depressed or if someone is anorexic and won't stop starving themselves then no they don't have a "right to die". Chances are good if we stop them from dying even forcefully they will come to thank us later.
All rights, all matters of morality and ethics are ultimately subjective. But subjectively I would not want everyone to just be like "OK, you can die" if my motivation was depression or if I was starving myself to death for beauty. I can imagine a lot of other people would want to be rescued from making such a bad choice too.