It's all about the internal stresses.
People who champion air dried argue that the wood loses moisture at a slow and varied rate. As the wood is drying, the weather changes, so the moisture loss is always fluctuating i.e. the wood loses a little moisture during the day, then gains a little at night, loses a little during hot days, gains a little during rainy days etc. This allows the core moisture content to catch up with the skin moisture content and in theory should reduce the internal stresses to the bare minimum.
Modern kilns try and duplicate this at a faster rate.
We use a lot of hard maple from North America and a lot of bubinga from Africa. The maple is pretty predictable, the bubinga moves around a little more after it's cut. This could be directly related to the properties of the wood or it could be that kiln technology is better in North America. We had a couple hundred bft of pau ferro that was extremely case hardened. It was perfectly straight in the rough, but when we tried to re-saw it, it cupped and bowed so bad that the last 1/8" would crack and break off before the saw had a chance to cut it.