Yukari says:

It’s a very good question and I think it ties with the strong National Identity that all Japanese feel, combined with the fact that in Japan, National Identity (being Japanese national) has for a long time also meant being born in Japan, by Japanese parents, with Japanese roots (cultural and racial identity). So half stick out and face a different set of challenges.
At the same time, when living in a country with a longer history of integration and a more mixed population and somehow less of a single cultural identity, the Japanese side probably felt as a clearer identity than the one of the other side, helping giving a better idea of oneself.
It is probably different when the other half belongs to a country with a strong identity as well, and you are growing up there. In such a case I would expect that being half Japanese could be somewhat irrelevant.