It is normally assumed that homochirality was the result of a reproduction/selection process. Once you have a self-replicating peptide, it will replicate its original handedness. As this replication process continues and builds more complex polymeres, you can imagine that they will reflect the chirality of that first replicating peptide.

Leslie Orgel in his article suggest another mechanism: Self-assembly on two-dimensional surfaces, like clay or minerals. This also can lead to the domination of a certain handedness.

The above mentioned homochirality mechanism by reproduction was experimentally verified in 2001. See http://www.scripps.edu/news/press/021401.html.

I did attack the website not only because of its obviously wrong statements, but also because of its dishonesty. I think "attacking the source" is justified in such a case.