No. For several reasons.
One is that there is a natural progression of grieving and death. When that progression is cut short then there are psycological issues that are nearly impossible to deal with. It is similar to people who have had family members murdered. The cut is so sudden that it becomes impossible for many to come to terms with their loss. Likewise the people who are dieing do not have the time to come to terms with their own death. There is a progression of stages that occurs naturally in order for someone to come to terms with dieing. While it is different for different people it is common for one of those stages to be the "I just want to get this over with" stage. Usually it occurs just before someone is ready to accept what is happening. By ending their life before they can come to accept what is happening they and their family will have their mental progression cut short and ensure that it will be a tramatic experience for both the patient and those that survive them.
Stages of Grief
* Denial (this isn't happening to me!)
* Anger (why is this happening to me?)
* Bargaining (I promise I'll be a better person if...)
* Depression (I don't care anymore)
* Acceptance (I'm ready for whatever comes)
* Numbness (mechanical functioning and social insulation)
* Disorganization (intensely painful feelings of loss)
* Reorganization (re-entry into a more 'normal' social life.)
The other reason is entirely religious. As someone who has seen the natural progression of death I firmly believe that there is a time appointed for us to die and if we hasten that unnaturally we miss out on experiences and blessings that God intended for us.
But as I said. These reasons mean nothing since in this imperfect world Euthanasia is simply a blank check for murder on the part of unethical people be they family or physicion.
It is significant that this is not a new question. As far back as Hippocrates it was a sufficient issue that the Hippocratic Oath includes:
"I will give no deadly medicine to anyone if asked, nor suggest any such counsel;"
An oath that physicians used to take in order to be trusted and upon which medical ethics are supposed to be based.
Just as it is significant that every society that has legalized eutanasia has ended up going the same direction that the Netherlands is right now.
Those who cannot learn from history are doomed to repeat it.