You are righter than you know. This is the proper "angle" of retort. It leverages the Culture of Death's confected "Right to Die" against them.
It is possible to believe, as I do, in the political right to kill yourself (not right to die, which implies others can help), while simultaneously believing in absolute moral prohibtion of suicide. This is so because we have property rights over ourselves, which includes the right to destroy.
Some confusion may apply here, considering property rights are legitimately prone to various restrictions, one of them being for instance that though property implies right of sale or transfer, we cannot legally sell ourselves into bondage. This is so because it would be to abrogate our right to liberty, which is inalienable; that is, nontransferable. The similar right to life is also inalienable, and seems to be threatened by suicide in the same way slavery threatens liberty. Ah, but though we end life by killing ourselves we do not sacrifice the right to life. For how can that right be alienated when it is I who kills me? It can’t be.
I consider anti-suicide laws a moral transgression even though suicide itself is perhaps the gravest of all sins. Certainly it is the only inherently unforgivable sin. But that is no concern of the law, in the same way it is none of their beeswax what spirits I put in my body, even though being a drunkard is a moral lapse.