Symmetry by subdiv proxy is done to the local coordinate of the object.
You use the Instance option of Duplicate when you make the object symmetrical
around the origin of the world coordinates.
You use the Instance option of Duplicate when you make the object symmetrical
around the origin of the world coordinates.
For the explanation about polygon modeling, please refer to
Maya tutorials: polygon modeling (1) basic operation
Maya tutorials: polygon modeling (2) operation of the polygon mesh
Maya tutorials: polygon modeling (3) Subdiv Proxy
symmetry by subdiv proxy
When you make the polygon mesh like the above figure symmetric by subdiv proxy,
the object is made symmetrical at the point where X coordinate is minimum.
symmetry by instance
Proxy > Subdiv Proxy 
reset settings
make a subdiv proxy.
Select both the smooth mesh and the proxy mesh.
Edit > Duplicate Special
select Instance at Geometry Type, and set -1 to x scale.
push the Apply button
They become symmetric around x=0.
Japanese article
Maya tutorials: polygon modeling (3) symmetric modeling by the instance
