Asian countries and cultures generally have stronger and more rigid notions of family than western nations. Newly married couples in Japan are officially members of one family or the other - not both - and being a member of the family includes obligations to care for the graves of the family ancestors. When a family has no sons, the eldest daughter may need to marry a non-eldest son willing to join the daughter's family and take on their last name. Otherwise, the family will die out, and there will be no one to care for the ancestors' graves. Per the article, it seems in about 5% of marriages, the man takes the woman's name.