when is it time to put an animal down?

Hi all, I’m not sure how many of you will feel about this post, but I need to share my feelings anyways. I am 21 years old and have had this cat for about 20 years, he’s practically as old as I am. I have had a love hate relationship with this cat my entire life, and there’s only one word to describe him since he came into my life; an asshole. His brother “Romeo” was the complete opposite but sadly went missing when I was about 15 years old. These days, the old mean cat can barely do much of anything, is losing his mind and began releasing himself anywhere he could, so we started letting him out during the day, and crated at night. Here is where things get pretty sad. Lately, he’s struggling to walk, is often followed by dozens of flies and is probably the most depressing thing to look at ever. One of my family members these past two days have demanded that he “stays in the crate”. Well, it’s day two and it’s starting to eat at me every time I go out into the garage and hear a few cries and see the dark crate where he’s just laying, basically waiting to die. She says it’s because he needs to be supervised when outside alone (we have a pool so this makes more sense). I can’t help but think this is a little cruel, keeping an animal alive to the point where flies are eating at him and he can barely stand and really think we just need to put the poor thing out of his misery. His hair is matted, he smells terrible and makes everything around him smell terrible, he’s basically all fur and bone. He’s basically pet cemetery irl and it’s equally terrifying and disgusting as it is straight up sad and inhumane. How do I go about this issue? He doesn’t deserve to be in such disgusting conditions but there truly is no other option.