Well, I don't know anything about this because I've never asked any Western/Caucasian men why they married a Japanese wife, but I'm saying my view anyway because I'm obnoxious like that.
-- Could be because the guy moved to Japan, happened to meet a Japanese girl (no surprise there, then!) and they fell in love and got married.
-- Or perhaps the girl was attracted to the guy because he was all hairy and "manly"! Umm, superficial much... but I think y'all know what I'm saying... actually this point (and the next one) is a bit like my first point except that in these cases the attraction was based on looks, not personality.
-- Maybe he was attracted to the girl cos she was littler/cuter/prettier than the majority of women he'd met in his home country.
-- Maybe the guy had the stereotype of Japanese women being more "feminine" and/or more submissive than Caucasian women, and deliberately sought out a Japanese lady (even if he didn't live in Japan). Well, this kind of relationship is really shallow, but in some cases it can (and does) lead to a marriage, so it can't be completely discounted as a "reason" for such marriage. .............. Even though this really isn't true these days! (I think some guys are living in the past a bit...

) ......... Oh, and this also includes those with an "Asian girl fetish", which are pretty rare IRL I think, but not unheard of.
-- Maybe the girl wants to marry him if he is rich, and she didn't find a Japanese boyfriend with money or good career prospects. Again, way shallow, but not impossible.
-- One good point many people made already - the world is getting to be a smaller place, communications are getting better, people do more travelling, so quite simply it's easier to meet people from different countries. Also, better communications help to break down stereotypes about people from other cultures. ............ This doesn't explain why there are more Caucasianmale-Japanesefemale couples than vice versa, but I can only say that the other way round relationships are also more common now than they would have been 50 years ago. Maybe because even in Western countries women didn't have so much freedom until recently, so they are still "in the process" of becoming more "exotic" in their choices of partners? :?
-- Another good point is about mutual interest in each other's country / culture, which could lead 2 people of different cultures to a closer relationship under circumstances where they might not otherwise have struck up a relationship at all (e.g. at work, and if the girl or guy is not striking in the looks department, you might not have given him / her a second glance in a bar, for example, but if you were interested in their culture or language you might make a special effort to talk to them in the work place, leading to a friendship and possible relationship).
-- I can't think of any more. :sorry: