Actually I think you could make a very indepth study of this. America has not always been this way. The first bicycling craze of the 1880s and 1890s was huge in this country. Bicycling was also seen as a key element in the womens' suffrage movement around the same time. Bicycle racing was quite popular in this country in the early 1900s as well (the Madison event was named for 6-day races around the original Madison Square in NYC).

Personally, I would try to find correlations between the advents of the rise of Hollywood, the massive change in direction of our culture after WWII, the rise and subsequent domination of television, and most importantly, the rise of car-culture in America. Lest we forget, there was a time when our country was not only more accepting of bicycles, but was a world leader in passenger rail service. All of that has been hugely eclipsed by the highway and a gigantic car-market infrastructure. You have to assume that it would affect culture as well.

Other countries have different viewpoints on cycles. I would assume that they also have vastly different cultural icons. The point is that the US was not always this way. It happened over the latter 2/3 of the previous century.