While I was studying in China, I noticed many Chinese woman-European man couples on campus, but I never ever saw a Chinese man-European woman couple.
I was very intrigued by this discrepancy - I find Chinese men very attractive and cannot understand why there are hardly any of them who were dating interracially while Chinese women didn't seem to have any difficulty finding non-Chinese boyfriends. I asked my American friend why she thought this was the case. She said she didn't know, but she said she would ask her friends to see if they had any idea why.
So my American friend went around asking fellow American students who were also studying in China why AWWM is far more prevalent than AMWW. She reported back to me that all of the white boys she spoke to evaded the topic and offered no answers. They seemed uncomfortable addressing the issue.
Then she talked to her black American guy friend, who said, "American men, especially white American men, see the Chinese woman as a trophy they can take home and show to their friends, saying, 'Look at me, I have an exotic Oriental doll on my arm. By the same token, the Chinese woman can show off in her social circle - look at me! I am dating a white American', with all the associated notions of 'white' = 'power, wealth and beauty'. AMWW, on the other hand, does not have the same level of trophy status for the parties involved.
I think he is right on although I am not saying this is the case for all AWWM relationships. It is worth noting that the black American is the only American male who tackled the question head on and gave his honest opinion.
Middle Eastern Student in China, 2001
I had a white American female friend who lived and worked in Japan for 4 years. She told me during that period, not a single Japanese man hit on her. And my friend is an attractive and friendly lady. She observes that Japanese men are generally more modest and less thick-skinned than Western men, and less likely to take an aggressive approach in pursuing women. Perhaps that explains, at least in part, the discrepancy between AWWM and AMMW numbers.