y'all are wayyy overcomplicating this - she just heard a friend in a relationship say that "when you love someone, you can't think about anyone else" and took it at face value (most likely because she doesn't have any prior experience when it comes to this, so this is all she has to go off of), she's taking care of her brother -> she can't afford to not think about him.
that's it. that's her entire thought process. I'm willing to bet that if that same friend tells her that she didn't mean it like that and that she'll be fine with him, then she'd be willing to date him.