A lot of them want a son to "carry on their genes/carry on the family name", which is considered important in Japan because of the focus on family/social status.
This has changed a loooot in the Heisei era, due to goings-on with the Imperial family. Basically, the current Crown Prince Naruhito only has a daughter, Princess Aiko. In fact, the entire Imperial family went
41 years without conceiving any male heirs.
In 2006 a distant member of the Imperial family gave birth to a boy, but there's some debate about whether or not a cousin should be third in line for the throne based only on maleness. As late as 2007, Japanese politicians were still debating amending the national constitution such that the Imperial line is one of equal primogeniture, which would move Princess Aiko into third in line for the throne.
The Imperial line is supposed to be descended directly from Amaterasu. A lot of people decided that if the Imperial line went 41 years with only daughters, then clearly that was some sort of divine sign about the value of having daughters. The situation has sparked a resurgence of interest in the Himiko legend and has become incorporated into Japanese feminist discourse.
The Himiko legend is a super-ancient story about how the only time ancient Japan was ever peaceful was when it was ruled by a mysterious woman named Himiko. After she died she was briefly replaced by a male leader and the country immediately descended into war. The people were so outraged that they rose up, murdered the warlord, and installed Himiko's daughter as the new Empress.
The interesting thing about all this is that the oldest known historical records referencing Japanese civilization, which are archived in China, do actually mention Japan as being ruled by a woman whose name could be translated as Himiko or Pimiko. So there is actually a historical reason to believe that Japan was at one point a matriarchal society.
(This would certainly explain some things, like how Japanese family property traditionally inherits along the matriarchal rather than patriarchal line.)