Population isn't really the root of the problem (though there is a carrying capacity to the earth, of course), it's our consumption levels. Specifically, western Europe, North America, Australia, etc. The West. Y'know, the countries that ruled the world during the industrial revolution and for quite some time after.

I=PxAxT where I: Environmental Impact, P: Population, A: Affluence, and T: Technology.

This is obviously a simplified formula, but it's a useful one when doing environmental impact analysis at a macro level. If everyone on the earth consumed resources like the United States, then we would require more than 3 earths to fuel our desires. Since there's huge wealth disparity, resource shortages hasn't happened quite yet in 1st world countries.

Bikes aren't really an issue in the grand scheme of things. Cars are. Massive cargo ships and international trade of basic resources instead of trying to rely on local sources is a big problem. Bicycle transport and its environmental impact pales in comparison to all other forms of transport, besides walking. Racing is sorta a fringe thing, and I doubt that carbon fiber will replace aluminium (an infinitely recyclable material), or steel, for most bikes.

Would be interesting to do a little research to investigate this topic though, and really find out which material is most "green".