No, you're not losing me. I think anyone who's ever had to face this situation goes through a similar mental adjustment. I don't know if it's a consolation or not, but the subject is one that I think people who have to do this for a living revisit from time to time. It's something you change your stance on. And re-adjust.
As for the other part of this...
Should your relationship with the person matter? It depends on the situation. It depends on your resolve. It depends on how much you loved him. It depends on if you're the only one there to do it. It depends on if it 'needs doing'. It depends on a lot of things.
I've been in your situation twice. I've pulled the trigger once.