Why do we need a sphere to graphically represent a qubit?
If we have $a|0\rangle + b|1\rangle$, there are two quantities we need to know to specify the qubit: 


the ratio $a/b$, which is encoded by the latitude: $\left|0\right\rangle$ is the north pole and $\left|1\right\rangle$ the south,
the relative phase of $a$ and $b$, which gives the longitude. 


That is, you can treat either $a$ or $b$ as a real number, but not both. 

A circle can only specify one quantity.