NMR Splitting for Adjacent, Equivalent Hydrogens?
There are two ways to look at this.

a) All transitions you can see are between a state where the spins are parallel and a state where they are antiparallel. 

$aa &lt;--&gt;  ab$  or  $ab &lt;--&gt; bb$

Their distances are identical, as are the states $ab$ and $ba$, so, as porphyrin said in his comment, you only see one line.

b) If the two protons were chemically different, you would see two doublets.

If the difference in CS were small, you'd see the "roof effect": An AB spin system. The two inner lines come closer and grow at the cost of the outer lines.

But there is no difference in CS, and so the outer lines vanish, and the two inner lines coalesce into one singlet.