in CC3 "Edit Mesh mode", select vertex at right-side of face and push "Mirror Selected" button, vertex at left-side are selected.
But I move vertex at right-side to right, then vertex at left-side move right, too (not oppsite/mirror direction, just same direction).
so these vertexes cannot be edit same time at left-side and right-side.
Is there any way to edit mirroring?

Welcome!
I am afraid this is a bug and should be entered into Feedback Tracker. Please submit your first issue and hopefully it would be fixed in the next patch or release.
https://www.reallusion.com/FeedBackTracker/

UPDATE: I just checked CC2 and it has the same problem. While I never used CC2 to edit mesh because of very basic implementation, I might in CC3 since it's a bit more advanced.
This issue is very critical if you need precision in symmetry. And while at it, the sculpt brushes also need a mirror option.