"I'd rather read a book that you liked. Wouldn't it be troublesome to search for a book you think I'd like?"
Actually makes sense. He wants to get to know her better, and this approach works in service of that objective.
I said it last time, but they're actually in position to kiss. Too bad this seems exactly the kind of moment where Hanabi will show up to ruin things.
Here's a better idea. DO IT. Even if Hanabi shows up, ignore her and kiss Fumi. Right in front of her. Assert your freedom from her.