The interesting aspect of Japan's "apology first" culture is that it doesn't necessarily mean you have some interior sense of sorrow when you apologize - quite often it is simply a way of smoothing over social situations in Japan.
Even if a person didn't do anything wrong, saying "I'm sorry," is a way to maintain harmony and avoid needless embarrassment or awkwardness at work or in some other Japanese social situation.
The apology culture of Japan is also on display in a unique way in corporate leadership. If, for example, two factory workers die on the job because of company negligence , the c.e.o. is expected to go to the home of deceased family and apologize profusely by bowing and appearing very contrite; and the event will be covered on TV and done in a very public way.
This aspect of Japanese culture exploded on the shores of America a few years back when a U.S. Navy ship mistakenly rammed into a Japanese ship with several school children on board. It was a tragic situation and several people died.
Justice ran its course during a court martial in Hawaii, but for the Japanese a court decision wasn't enough. There was a clamor for the American Navy Captain to fly to Japan and personally apologize to the family of the people he accidentaly killed.
Yet the irony of this is that in much of Asia (mostly among the political class), there is still anger toward Japan and the Japanese government for not apologizing for Japan's Word War II aggression.
There are a few lessons from this that foreigners, and ESL teachers in Japan can take from this apology culture. Toshiya Enomoto writes about the Japanese language and apologizing:
"Japan's 'apology first' culture makes it possible for gaijins (foreigners) to get out of most jams with sumimasen. Sumimasen...is equivalent to 'excuse me.' It is, however, just as useful for apologies and some Japanese prefer to say sumimasen as they think it is a more refined apology 'for grown ups' than gomen 'nasai. Saying sumimasen is also a clever way for gaijins to hide their limited vocabulary."