The reason I think it may be a mistake in translation is because it might be easy to confuse the term for identical brothers for twins in some languages. Meaning when the MC says they are "twins" in the original text the term may be one for identical brothers or one that can be applied in both cases. Otherwise you have to presume a freak occurrence as CookieMonster is doing, and that is without even knowing if they would actually separate brothers scholastically under those circumstances. Korea already traditionally has a different way of counting age, and probably also has the Asian calendar as well. When it comes to schooling I believe the follow the Western calendar for practical purposes, at least as far as age is concerned.
Im confused arent they twins?? why is jo han kim a year older?