Denti,
Symmetric aerofoils and symmetric load cases are not directly related and vice versa.
The outside profile of an aerofoil determines the wing / lift characteristics. The dcl/dalpha curve is a factor in wing loading but the internal structure of that aerofoil can be tuned / skewed however you need it to match the load cases. So I can tune (which is what PDR stated earlier) the internal structure within a given external profile to match whatever you want (within the laws of physics).