FatBallsAndSunflowerSeeds Something I think I've realised as you get older (ha! I sound ancient), is that 'you feel how you feel'.
My Father only passed away last September, yet I can already talk about the day it happened and actually managed to write and deliver his Eulogy a few weeks later in the Crematorium.
I genuinely don't think I would have been able to do that with my cat - Even now I can feel sad from time to time, however I do think my guilt isn't there as much as I can look at things from a more subjective viewpoint, e.g. He had lost so much weight, when the vet came to put him to sleep she said she could smell his litter tray (apparently that's also a warning sign) and he just wasn't happy.
My Dad and I didn't have the best relationship in the world and to be fair, my cat was an absolute arsehole (urinated constantly EVERYWHERE, destroying 3 houses over 8 years), however I loved both in my own way.
I honestly believe that what we, and so many other pet owners have done is the most unselfish thing possible - Unfortunately my parents weren't able to do that and they didn't take their 19 year old cat to the vet, despite her struggling (I wasn't living at home and didn't know this until afterwards). She died, probably in pain - because my parents were trying desperately to not have to deal with the pain of losing her.
However I guess that pain will always occur at some point, so why prolong any suffering? We'll always want 'one more day', but when it comes at a cost of pain... That's when you need to say 'No, this isn't right'.
One thing my partner and I have always agreed - When we take our cat to the vets, the only mantra we need to have is 'Whatever is the best for our cat' so even if we don't want him to have an operation / be given drugs / be put to sleep (potential in future, who knows?) we must do what's best for him, regardless of how that makes us feel.
The pain is real and all you can do is take one day at a time and be kind to yourself.