I actually saw this on the news and I didn't like the argument against allowing this.
It's not something that I've considered in great detail so this is just a superficial reaction (at the moment).
Arguments against were based on morality, religion, and personal opinion.
The thing is, this is not being proposed as compulsory, merely as a right to die for terminally ill patients at a time of their choosing.
So, in principle, should people, who are terminally ill and facing a short future that offers increasing pain and suffering before their inevitable death, be allowed assistance in achieving an early death?
I believe they should, and I can't see any good reason why the choice should be denied them. If they are religious, or have other oppositions, they're free not to take up the choice.