The Story
When cooking pasta, it's important that we don't add it to the water until it has reached a full boil. After that, we must stir until it is fully boiling again, and then keep it boiling until the pasta is cooked. Anything else will ruin it.
Facts
Cooking pasta consists of two independent processes: the dry pasta must be rehydrated by absorbing water, and the raw flour must be cooked by the heat. This is complicated by the tendency of pasta to stick together if left undisturbed in warm water.
If dry pasta is added to cold water and that water is heated up, the pasta will rehydrate with no problem. If boiling water containing pasta is removed from the heat, so long as there is sufficient water to retain the heat for a while, the pasta will continue to cook properly even if the water isn't boiling.
Why
The simple rule about boiling has been passed down for centuries, and since it works, no one questions its validity. The one thing that this rule accomplishes is to keep the pasta from sticking together. As long as the water is rapidly boiling, the individual pieces won't stay in contact long enough to stick.
But really, if you're willing to pay attention and occasionally stir it once it gets warm, you can start the pasta in cold water. And if you use a lot of water, you can remove it from the heat once the pasta and water are boiling. Or, better yet, if you use a minimal amount of water and keep heating it, the water will reach a boil much sooner (plus, you'll have a much starchier water, suitable for mixing with sauce to make it stick better).