Would it be wrong to suggest my mom puts her dog to sleep?

My mom has a 13 year old pit bull. He's lost a lot of muscle mass, and it looks like he's starving, but he's not. He pisses and shits when he doesn't even seem to realize it. Sometimes he just walks while doing his business. He has arthritis. My mom tried pills prescribed from the vet. She used those for a couple years but it didn't seem to be helping much, because he still limps up the stairs. I don't live at my moms anymore so I don't know if he still does, but several months ago, she started taking Him to the vet monthly to get injections for his arthritis. My mom says it's helping, but he stays at my place while my moms at work, because she doesn't want to leave him alone all day, and he walks around and whines like 90% of the day, and he's VERY Clingy. He i also have to pick him up on my bed, because he can't jump up himself. He just stands there and whines loudly. I don't know if this is all because of his arthritis, or cognitive decline. I don't know, I feel like he's just so uncomfortable, and my moms trying a lot. I don't know if I should suggest she has him euthanized? He just seems miserable.

Would it be wrong to suggest my mom puts her dog to sleep?
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