Degree-Days are funny fellows. Firstly there are two types Heating & Cooling Degree-Days. So to keep it simple let's just look at Heating Degree-Days...
As we saw previously, there is an outside temperature called the "Balance" when you don't quite need any heating. Think an early day in autumn (fall for our US brethren). It makes sense that it should be about the same as the temperature when you don't need any cooling either - so heating and cooling are in "balance".