In Europe you will hold open a door for a lady and you will allow the lady to enter the restaurant first. The Japanese don’t have this politeness rule; in fact in traditional Japanese culture men are deemed superior to women. This is totally unacceptable - but in Japan, that’s the way it is. I have the feeling this is changing a bit these days but it’s good to know.
In, 2012 a study by The World Economic Forum ranked Japan 101st out of 135 nations when it came to gender equality. The Japanese have a very traditional view of the family where the man is supposed to provide and the woman is supposed to take care of the family.
In practice as a traveller you probably won’t notice the gender inequality too much. A common situation where you might experience it is when as a male traveller ladies let you go first on elevators. Especially the older generation abides by these “rules”; younger people tend to act more Western i.e. men and women are considered equal.