By default
$x,y\in \mathbb{C}$ in Mathematica; therefore one has to shelter with
In[22]:= Last[ToPolarCoordinates[ReIm[x + I y]] /. {Im[x] -> 0, Im[y] -> 0, Re[x] -> x, Re[y] -> y}]
Out[22]= ArcTan[x, y]
if you do not fear the ugliness just type
In[24]:= Last[ToPolarCoordinates[ReIm[Re[x] + I Re[y]]]]
Out[24]= ArcTan[Re[x], Re[y]]
because still
In[27]:= Arg[Re[x] + I Re[y]]
Out[27]= Arg[Re[x] + I Re[y]]