Your argument is very weak. You said, “Not practicing euthanasia at the request of the dying person is violating a person’s rights, creating an economic burden, interfering with a doctor"s job…” This is a form of a fallacy that begs the question. No evidence is offered to support your claim. You failed to explain how not practicing euthanasia violates an individual right, creates economic burden, and interferes with doctor’s job. All you did was to make evidence your own claim, but in reality no evidence was given or any explanation for those claims.
It devalues human life. This is one reason why euthanasia is not acceptable. Proponents of euthanasia, however, do not believe it degrades life and for them patients who suffer from incurable disease should be afforded with a choice whether or not to end their sufferings. But the problem with that, it is not always the case, not all reasons for accepting euthanasia center on the suffering of a patient, other reasons are decreasing medical costs and other monetary reasons. For example, a report issued by EPAC, the Economic Planning and Advisory Council, a government think-tank. The report discussed the rising costs of medical care for the elderly, and rising hospital costs in general, and actually suggested that euthanasia might be an option in dealing with this crisis. There was no mention of suffering or the humane treatment of dying human beings. Instead, cold utilitarian considerations of cost-cutting were given as the reason to consider euthanasia.1
That becomes problem when reasons, other than the suffering of the patient, are given in support with euthanasia. It degrades the life of person by saying that his life is less important than the money that might be saved if euthanasia is accepted.
Life is very sacred, accepting euthanasia destroys that sanctity. It may be your life but according to God, you don’t have the right to take it.
Another reason against euthanasia, It neither preserve human life nor protect the mentally ill and disabled from medical malpractice and coercion
In Washington v. Glucksberg ,the Supreme Court of the United States unanimously held that a right to assistance in committing suicide was not protected by the Due Process Clause.2
Chief Justice Rehnquist wrote the majority opinion for the court. His decision reversed a Ninth Circuit Court of Appeals decision that a ban on physician assisted suicide embodied in Washington's Natural Death Act of 1979 was a violation of the 14th Amendment's Due Process Clause. The Court held that because assisted-suicide is not a fundamental liberty interest, it was not protected under the 14th Amendment. As previously decided in Moore v. East Cleveland, liberty interests not "deeply rooted in the nation's history" do not qualify as being a protected liberty interest. Assisted-suicide, the court found, had been frowned upon for centuries and a majority of the States had similar bans on assisted suicide. Rehnquist found the English common-law penalties associated with assisted suicide particularly significant. For example, at early common law, the state confiscated the property of a person who committed suicide. Like Blackmun in Roe v. Wade, Rehnquist used English common law to establish American tradition as a yardstick for determining what rights were "deeply rooted in the nation's history." Rehnquist cited Roe v. Wade and Planned Parenthood v. Casey in the opinion.3
The Court felt that the ban was rational in that it furthered such compelling state interests as the preservation of human life and the protection of the mentally ill and disabled from medical malpractice and coercion. It also prevented those moved to end their lives because of financial or psychological complications. The Court also felt that if the Court declared physician-assisted suicide a constitutionally protected right, they would start down the path to voluntary and perhaps involuntary euthanasia.4
Similarly, in Vacco v. Quill, the Supreme Court of the United States ruled that a New York ban on physician-assisted suicide was constitutional, and preventing doctors from assisting their patients, even those terminally ill and/or in great pain, was a legitimate state interest that was well within the authority of the state to regulate. In brief, this decision established that, as a matter of law, there was no constitutional guarantee of a "right to die."5
   http://en.wikipedia.org......