Why might chopped meat make me sick?

Intestinal bacteria that contaminate meat contaminate that portion that is exposed, namely the surface. In general, when the exposed surface of meat is heated adequately (that temperature varies with the kind of meat -- see http://digestive.niddk.nih.gov/ddiseases/pubs/bacteria for guidance -- but a ballpark figure is 165 degrees F), the bacteria are killed.

There are two problems with chopped meat. First, the inside is the outside, and vice versa. Chopping meat massively increases the surface area, allowing the bacteria to invade throughout. And, because meat at the very center of a burger, patty, meatball, or meatloaf could well have been on the surface at some point, contaminating bacteria are only reliably killed if the temperature throughout reaches the relevant threshold. Because the entire area of chopped meat is surface area, it should be eaten well cooked.

The second issue with chopped meat is that it generally comes from multiple animals -- in the case of ground meat prepared at centralized processing facilities, possibly quite a large number. The risks of bacterial contamination rise in this situation, because even one infected animal may contribute germs to meat being sent all over the country. When you eat unchopped meat, the source is a single animal.