On Nemo, if you try to move a file by cutting and pasting from one directory to another, it will silently fail if you don't have write permission on the directory where the file is contained. This can happen, for example, if you create a secondary user for testing purposes and you add yourself to this test user's group so you get read access to their home directory. Then you can read and execute call directories but you can't write to them [What Read, Write, and Execute Permissions Mean on Linux].
Copying and pasting the file, on the other hand, works, since this doesn't require modifying the file list of the source directory.