I would say the argument comes down to how you value life. Those most opposed to euthanasia are likely to hold the belief that all human life is equally valuable, and there is no such thing as a life not worth living, and to support euthanasia and assist someone in actively taking his or her life, is to abet them in the mistaken belief that their life is not worth living.

The typical response to this is that euthanasia opponents are living in a dreamworld, and lying to themselves. It is obvious at its face that some lives are not worth living, and to think otherwise is foolish.

On the other hand, the euthanasia opponent can reasonably ask how can we both support euthanasia and have suicide prevention hotlines? The existence of both seems to indicate that our societal response to an eagerness to die, rather than being about individual choice, is more about encouraging cultural norms about who is to be valued.