Doesn’t need to be anything too deep; an appreciation of quiet by itself would make sense, given his family background. We don’t know if/when the birth mother went out of the picture and the new one entered, but it’s somewhat safe to assume it was at least a couple of years. Youta would be used and comfortable with a quiet home. Then the step mom joins the family, which is a tricky thing for a child to deal with, but let’s say early tens for Youta. And then the twins get born. Suddenly everything is loud, everything revolves around them, and just dealing with toddlers and pre-schoolers, and a pair of them at that, is always a handful.
Whereas before the home was a retreat for Youta from the stress and demands of school, now it is a different set of stressors and demands. This is not to lay blame at the mother’s or the twins’ feet, it’s simply how it is. It’s a good thing Youta doesn’t seem to have much teenage drama going on personally, unlike Koyuki or Minato for instance, because if he had, having no place where he can simply be, without needing to take children or peers into consideration, would be… well, definitely worse than his current situation. As is it’s likely he’s striving to move out as soon as possible, if only to get some semblance of privacy and mental space.