Can you confirm that you problem ran to completion with no errors?
In 2013 Sp3.0 it runs and is as symmetric as it can be with a coarse draft quality mesh. Remember there will be some asymmetry because the mesh cannot be guaranteed to be symmetric. You could go with quarter symmetry in this problem though to get even closer to perfect symmetry.
Hi Jared ,
Yes, the analysis ran without any errors.
I even contacted my reseller about this issue. Seems to be some bug in Solidworks 2012 SP 1.0.
Updated my service pack to 2012 SP 5.0, the displacement is fine and symmetric.