For example, consider what happens when averaging (0,1) and (0,-1) in cartesian coordinates vs polar coordinates. In cartesian coordinates you get the midpoint at (0,0), but in polar coordinates both have the same length... so you just get a point a (1+1)/2 distance along (0°+180°)/2. That's either (1,0) or (-1,0) depending on the handedness of the coordinate system, off to the side instead of in between!

The same effect happens in RGB vs HSV.