Why can't I loop cut all the way around the object? How to make a loop cuts all around the object? I can select just one side and I need them all at the same time.



Here is what I need.
If the mesh already is triangulated you could use the Knife tool (K) in Cut Through (Z) and Angle Constraint (C) Mode when you are in a side orthographical view. This will let you add edges regardless of the topology.

But most of the time it's better to just un-triangulate it manually by Dissolve edge or with Tris to Quads (Alt-J) in the face menu (CTRL-F). 

If you have ngons you can find them with the Select All by Trait/Faces by Sides and set the number of vertices to Grater than 4. 

You will find it much easier to work with quads.