Great inhumanities are usually ushered in at the extremes in order to make the public more accepting. Abortion on demand followed the 1973 Roe v. Wade case where Norma McCorvey, Jane Roe, "alleged" she had been raped, resulting in pregnancy. Technology allows people to abort a "defective" baby in the womb, "selectively reduce" implanted embryos to the desired number, or even abort a female when a male is wanted.
Euthanasia will not originate with your beloved grandmother or parents. It will start in a public hospital with a 100-year-old woman who has multiple health problems and "wants" to die so as not to "burden" anyone. Public opinion polls will determine that a majority favor letting -- even helping -- the old girl die.
Yes, there are times when a patient and his family may decide to forego treatment and allow death to occur, but that decision should not be made by a government official. Once that door is opened (as it was with abortion) there will be no closing it and dying will become a patriotic duty when the patient's balance sheet shows a deficit.
They'll probably have a clergyman available to bless the government's decision and make everyone feel better about it.