Why? Because you can't stay here since you're the only one your sister has left and she certainly won't want to stay here. He can't come with you to Japan because he'll be an illegal immigrant in Japan. Being an illegal immigrant in Japan is a terrible life, he'll be taken advantage of his entire life, assuming he didn't get deported first.
Treating it as a summer fling is the best outcome for everyone.
Considering Titania managed to send them back to Japan easily can't they stay half the time in one world and the other in the other world? Take a third option!
@moonshadow Timeywimey shenanigans. She's been here for months now, but the time she arrived in Japan seemed to have been maybe days after they got sent to the other world. People are going to notice if you start aging rapidly or disappear for years at a time and come back younger than you should be. It sounded like using the spirit world as a relay point would have unpredictable results.