Don't forget, in the manga, his parents also thought it was a good idea for him to study away because of his close relationship with his little brother (RE: story were Izumi told Shougo he could go ahead and eat him while lifting his shirt).
Oh you think
the 3 years "journey" of Shougo was not about studying abroad. It was his idea of surpassing his father (being a great performer without the help of his father) and to make Rei look at him. And the idea of his parents letting him study abroad was when the time Rei was not yet with Sena's family.
Shougo left for three years because he was determined to make Rei fall in love with him. They have actually been together since Shougo was 15. I would suggest reading what has been translated of the light novel so far http://backstage01.pressbooks.com/