It's simple, really. Neither one wants to admit fault. Getting a "no
fault" divorce without the courts isn't good enough because people
could still speculate as to who was the guilty one.

Both feel having a judge decide gives them the best chance of having
the other blamed for the divorce.

In Japan, divorce is a very delicate subject. Usually, both "agree" to
split and no court intervention is necessary. In this case, it seems
neither can bear the appearance of impropriety and is looking for a
judge to blame the other person.
At least that's what it seems like from the info given.