Origin is not in the horizontal middle for a model which I "overlaid" I'm trying to set the origin of a mesh to the center.

Originally the rocket and the launcher were stacked over each other:



I have "put" the rocket into the launcher.

I have used Object -> Set Origin -> Origin to Center of Mass (Volume), and it resulted in this origin:



The arrows that I have added in GIMP reveal that there's a problem, as they don't have the same length.

What might be the problem here?

I have uploaded my Blend file here.

Thank you so much!!

Edit: Here is a screenshot of where the 3D Cursor is for me after I have clicked "Cursor to Selected":



The 3D is not centered vertically. What might go wrong here for me?
Further to @cegaton's answer.. the behavior of Shift S Cursor to Selected respects the current Pivot point.



in Edit Mode with all selected:


if the Pivot is set to 'Median', the cursor goes to the location of
the smaller empty in the illustration, at an average position of of
Suzanne's selected vertices, giving them all equal weight. Since she
has more vertices in her face than at the back of her head, that
drags the location towards the front.
If the Pivot is set to 'Bounding Box' the cursor is sent to location
of the larger empty, at the center of Suzanne's bounding box.


I'm not sure if this is what you want, but illustrated below is the result of Shift S Cursor to Selected in Edit Mode, with all vertices selected, and the Pivot set to Bounding Box Center, followed by  Shift Alt O in Object Mode > Origin to 3D Cursor



The cursor and origin are at the center of the object's bounding box.

The "Bounding Box Center" option is located here: