Why does a car exhaust rust much faster then other car parts?

The exhaust suffers badly for a number of reasons:

1. It is very exposed to water, debris, salt and damage from materials thrown up to the under body
2. They are made of relatively thin steel, with usually only a thin coating or none at all. The heat generated by the exhaust makes most paints burn off.
3. The exhaust undergoes extremes of heat and cold, as well as internal water vapour, all of which speed oxidisation.

There is the option of a stainless steel exhaust, which can last 10 years or more, but these are expensive to manufacture, so are generally not used on lower end vehicles.