Okay, wow. I spent my whole morning researching this, and I came up with five different answers, and I have no idea which one is the right one.
1. It's meant to slow down the eaters, like a QWERTY keyboard, by the constant switching of utensils, so people would remember to chew their food and talk to each other during mealtimes (it's debatable how successful this is, if this is the case)
2. Colonizing was dirty business, so the colonists adopted the Middle Eastern/Indian practice of reserving the right hand for eating and the left hand for the toilet (no idea how they would have known this, but eh), so mostly the right hand was used for eating in this method.
3. American colonists were so poor that families often only had one knife between them. By setting the knife down for most of the meal, it allowed everyone to have a turn with the knife. (This would explain the 'cutting with the side of the fork' thing Americans do that apparently no one else does, because you wouldn't take the family knife if you didn't have to, if it were true)
4. This way of eating is actually older, and the "European" style, always holding both utensils, came into fashion because of the French revolution/occupation/whatever. In the new style, you could see where the other person's hands were at all times, so you knew they weren't doing any treachery. Because this never happened in America, they never adopted the new style.
5. Probably the most convoluted one: England was the last of Europe to catch onto the whole fork idea, so when England began to colonize America, they knew about forks but they weren't in style yet, so Americans didn't use them until later. However, as forks became more popular in England, shipments of knives into America became duller, so Americans began to use spoons to steady their food while cutting it and then switching it back to the right hand because before these dull knives they would always wield the utensil with their right hands. (This would explain why this method is uniquely American if it were true, because pretty much nowhere else had this circumstance)