I think it's a complicated issue, and can't properly be declared entirely right or wrong. Depends on the individual case. Here's a bit about the debate surrounding the matter:
https://en.wikipedia.org/wiki/Euthanasia#Debate
Crudely speaking, the religious argument seems to boil down to the idea that their god says it's wrong. As I don't think there are any gods, for me that argument means nothing. And although 48% are religious in the UK, support for assisted dying exceeds 80%, which suggests that not all religious people in the UK are entirely against it.
If somebody is suffering horribly and there's no chance of stopping that suffering in any other way, then as long as they want to die, I think it's a kindness to kill them in a painless way. But we don't always know for sure that we'll never be able to stop the suffering without killing them, and sometimes people want to die one day and want to live the next day. And there's the question of who can be trusted to make these decisions - doctors may want to harvest organs or get problematic patients off their books, relatives may want to get rid of the patient or to benefit from their life insurance or last will and testament.
I think there's also a strong emotional abhorrence about killing somebody even if it's logically the action of choice. I once put a pigeon out of its misery. A cat had made a horrible mess of it and it was pretty obvious that it couldn't be saved. I still think killing it was the right thing to do, but I was very upset at the time and even now after about 40 years I feel tearful when I remember it. I think I'd have felt almost as bad if I'd just walked past it, though its suffering would very likely have been greater. I think morals are based on emotions, and emotions aren't always in line with reason. I hope I never have to make such a choice about a human or about any other sentient life-form.