Firstly, I completely agree euthanasia should be legalised and I find it as illogical as the next person.
I would not agree with someone suffering depression being euthanised. Depression is a disorder ultimately caused by chemical imbalances in the brain, and sometimes symptoms include suicidal tendencies. I would not agree that someone suffering clinical depression is on a par with someone suffering from, for example, MS or terminal cancer. If it were legalised there would have to be documented proof that the disease is untreatable, coupled with a psychological analysis of the person being euthanised to confirm they are mentally capable of making an informed decision. The exception would of course be with someone who is unable to communicate their wishes (i.e. someone in a coma), in which case that person cannot be euthanised unless they have made a legally viable will stating their wishes clearly.
There will ALWAYS be arguments against euthanasia - a lot of "what ifs" and "buts". What if a person in a coma changed their mind in their coma? What if someone uses it to their advantage in order to speed up the death of someone? What if God is real and we're sending our loved ones to hell? (For the record I believe the latter is a ridiculous argument, but you have to take all arguments into account).
In the end you have to weigh up the pros and cons of what is effectively legalised killing. Yes, if it were legalised, at some point in the future a horror story is going to crop up. Does that possibility mean hundreds upon hundreds of people of sound mind, with loving families, need to go through daily humiliation, indignity, pain and suffering for no purpose than to appease the sanctimonious minority? I don't think so.
By the way, you cannot say religion is irrelevant. As much as I despise religion, there's no escaping the fact it plays a massive part in the reason behind euthanasia being illegal. Th