This is a cookie related tutorial … why doesn’t cookie cares … but ok.
‘Set/Clear Inverse’ has nothing to do with this.
A parent can have lots of children but a child can have only one parent.
It means that … If dad is driving his car and mom hers, the child cannot be in both cars at the same time.
With the ‘Child off’ you have a bit more options but still …
In your file the ‘Axis’ already has tree parents ‘Child off’ and now you are adding an extra one. This is asking for trouble. The animation seems to work fine because all those parents seems to take control at different times in the timeline not interfering with each other. Now you added a 4th empty acting like a bull in a china shop. Taking control all the time while the other parents try to do their job and the cube has no idea to whom to listen to.
If you want to add an overall animation on top of the parenting thing you will have to find another way of doing it. You cannot have two empties (parents) at the same time talking to the cube telling it what to do.
If dad is the parent, driving his car and the child on the back seat, the child can play on the back seat but still has to follow dad in his car. If dad takes a corner, the child takes the corner too. I don’t know what action you want the cube to do but you can animate the ‘Base’ bone perhaps.
