This is one of the important arguments against euthanasia.The acceptance of one sort of euthanasia will lead to other, less acceptable forms of euthanasia. Pereira provides us with the slippery slope practices :
Initially, in the 1970s and 1980s, euthanasia and assisted suicide advocates in the Netherlands made the case that these acts would be limited to a small number of terminally ill patients experiencing intolerably suffering and that the practices would be considered last resort options only. By 2006, the Royal Dutch medical Association had declared that " being over the age of 70 and tired of living" should be an acceptable reason for requesting euthanasia.
.Until 2001, the Netherlands allowed only adults access to euthanasia or PAS. However, the 2001 law allowed children aged 12-16 years to be euthanized if consent is provided by their parents. By 2005, the Groningen Protocol, which allows euthanasia of newborns and younger children who are expected to have"no hope of a good quality of life," was implemented.
What is slippery slope ?
A slippery slope argument is a kind of argument that warns you if you take a first step, you will find yourself involved in a sticky sequence of consequences from which you will be unable to extricate yourself, and eventually you will wind up speeding faster and faster towards some disastrous outcome. . . .
Slippery slope arguments flourish where scientific or technical developments create new situations not covered by traditional terms, especially controversial terms like "death," "life," and "person." New options for defining these terms then become open to argumentation on issues of how the new technology should be used or limited. The abortion issue seems to be the most common example of this kind of argumentation.
 (Pereira.J. Legalizing euthanasia or assisted suicide: the illusion of safeguards and controls in Current Oncology. Vol.18, No.2 (2011). http://www.current-oncology.com /index.php/ oncology/article/view/ 883/618.
Slippery Slope Argument. by Douglas Walton. Studies in Critical Thinking and Informal Logic No. 4. http://www.valepress.com. Accessed 3/10/2011.