>>536341102
She wants to have sex with him.
No really. That's basically it. She wants his cock. Unfortunately for her, Shadow's a volcel.
But besides that, she probably feels pity for him since she looked through his files. She also might feel more like she can be herself around a male who flat out doesn't react to her flirting. Her charms just don't work on him, and maybe she likes the "hard to get" aspect, or thinks she can be vulnerable around someone like that since he won't take advantage of her. Rouge's value to Shadow has nothing to do with her body and that's something Rouge is not used to. I'd ask why she doesn't have female friends, but there's no option other than Amy, who she disliked originally because Amy was acting batshit. They're trying to make her and nu-Amy friends now.