What use does he even have for summer classes at his usual school? He's going to a cram school anyway, to prepare for the university entrance exams. He's getting full scores from the high school exams as it is, so there's technically nothing he would learn from those summer classes. It's not like the teachers there would teach him stuff from future courses. That would be pointless from the school's point of view. An external cram school obviously couldn't care less about his particular high school, they are only concerned about preparing him for entrance exams, to give him value for the money spent.
I reckon he was only going to the summer classes because studying was his only way of life and hobby. So, he was studying even if he learned nothing new. Socialising with Koira ought to teach him something, and if he helps her with her assignments, he can keep stuff fresh in his own mind as well. Not to mention this ought to give him motivation more than anything else: a young lad spending time with a cute girl.