Considering how the childhood friend really loves and respects him as an individual, its disappointing how much more he cares about some random girl he knew for a day. She clearly has done a lot to help him and keeps offering only to get rejected.
I imagine it's because it's too close to "more show business" for him, which might be too raw a wound coming off the still-somewhat-recent ejection from his family.
I absolutely cannot imagine that he's cutting ties with Asuka as a person - but he doesn't believe in himself or his abilities, and I suspect that being thrust into working for another company right away would just be too much stress, especially when all he wanted to do was "live a normal high school life".
He really does need time to just be a kid, because he's never gotten that chance. And even if the new company would be leaps and bounds better for him and
to him, it'd just be him giving up his "chance at youth" all over again.
Yeah, he thought of Butterfly Eyes right before he turned down the president's offer, but I don't really think he's consciously thinking romantically or anything - just in terms of what feels most comfortable to him in the moment. And Asuka can absolutely still come to him as a person; she would probably just do well to avoid trying to rope him back into her circle in a professional sense, at least for now.