You are plotting the value of a constant function on the sphere:
In[23]:= Sqrt[Spin2[SPIN, x, y]] // Simplify
Out[23]= 15
This way you get a sphere with radius 15. Your coordinates x,y are not cartesian: they fix a direction in space.
Compare what you get with PolarPlot[15,{theta,0,2Pi}]: this associates with every direction theta a radius with length 15, so that you get a circle with radius 15.
