I don't think that ageing is the reason. The Japanese birth rate (1.4 children per woman) is still higher than that in the neighboring nations such as South Korea, Taiwan and Hong Kong. Also, the Japanese life expectancy is much higher, meaning that the death rate is low.
At most, 1.4 would be two children. That's still too few to support aging parents if they also have to support their own families. Of course there's social security, but we all know it's mostly a Ponzi scheme where the current workforce is paying for the benefits of the retired sector.
In Japan, they normally work until 65-70 years. And the children and grandchildren do look after their parents and grandparents, rather than dumping them in some old-age home. And trust me, 1.4 is much better than the situation in the Chinese cities (where it is below 1.0).
If they're working up to that age then hopefully they've saved enough money for the family. Maybe it really is cultural.
As for China, this is a result of the One Child Policy. They are trying to reverse it now because of the aging population but it seems people are not interested in having more children.