Kind of funny because I don't think I ever was like, I am motivated to recover because of xyz. Don't get me wrong, I think it's a great question, it's just that I never thought of it that way before.
Whenever I've gotten help from mh professionals, I usually lay out what I want help with or want from them, but I don't usually think about exactly why, and I also hadn't really thought of it as recovery before, just getting help. Recovery seems to imply taking back what was lost and to return to a certain state, but it sounds a bit too ambitious for me.
I think the simplest answer, like someone else said, is to just feel better. Because it sucks to be hurting. And for however long I'm going to be here for, it would be nice if it were more bearable.
A more idealistic answer would be more something like, I want to have a net positive effect on this world, or I want to do what I can to help other people while I'm here. Not sure exactly where it comes from (though I have some ideas) but since I was a kid I always wanted to do something that could help other people and have a positive effect on them. It's hard hearing about people suffer when you feel like there should be something that could be done that would help them not suffer or suffer less.
Maybe because of who I am or what I've experienced, there are things that only I can do or say (although the skeptic in me tells me that I am infinitely replaceable). But nonetheless, if there's any part of me that could help someone or do something for someone, I'd wish I have the bravery and willpower to do it. Reality isn't always that idealistic, though, and as a human I'm pretty selfish and needy. Maybe that makes me more relatable to other people too, though? And maybe you'll relate to some of what I said, too. :)