Why 360 degrees is in the top instead of 90 degrees in aviation?
Conventionally, geographical maps are shown with the North up and North is also by convention 0 degrees (or 360), which is equal to the compass heading of North. The angle increases clockwise, with 90 degrees being East. This is not specific to aviation; in fact during flight the preferred presentation is to have the map oriented such that the direction of flight is upward. 

The mathematical plane you seem to describe on the left has the primary axis as the angular datum (also by convention, more info here and here). So the positive x-axis is 0 degrees. The angle increases counterclockwise, so the positive y-axis is 90 degrees.