Cleaning up. Staying there near him, means they will still be aware of each others like a scar that won't heal.
Moving away is like forcing a closure, they can restart, or continue like before they met each other. Easier to forget if the source of the pain is no longer there in front of your eyes.
Usually like that (too lazy to re-open the book to clarify)
Also, she has mental problem. If the environment could cause problem, the doctor could have suggested to move.
Being known as someone with multiple personality might bring unpleasant attention she still can't handle. Same with any other possible bad influence to her condition.
that leaves me with the question who does he really like? Is it akiha or Haruka?
For now, he still think Akiha is the girl he loves. Haruka is a friend he wants to help.
From the beginning, he falls in love with Akiha. Meanwhile, with Haruka he sees someone like him who tried hard to be someone else.
v2-6... spoiler