Subdiv proxy lets you simultaneously preview the smoothed version of the polygon mesh while you modify the original mesh. The original mesh appears partially transparent so you can view the smoothed version beneath. When you turn on Subdiv Proxy’s Mirror Behavior option, you can modify the original half of the polygon mesh while the other half updates.
To model a polygon mesh symmetrically using Subdiv Proxy

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The original mesh is mirrored along the Mirror Direction.

The modification automatically updates on the opposite half of the subdiv proxy.

After you have created a symmetrical model using Mesh > Smooth Proxy > Subdiv Proxy (with Mirror Behavior set to Full), use Mesh > Smooth Proxy > Remove Subdiv Proxy Mirror to remove the smooth mesh. Then use Mesh > Smooth Proxy > Subdiv Proxy (with Mirror Behavior set to None) once again to create a smooth mesh that you can animate non-symmetrically.