Maybe first try practicing creating a compound path with simpler paths.
Use the Ellipse Tool, select a fill color, draw one big circle, then draw a smaller circle inside it.
Next, use the Selection Tool to select both of the circles.
With both circles selected, click Object / Compound Path / Make.
At this point, you should now have a compound path.
The next step would be to determine why your objects won't become compound paths.
It's hard to say what the issue might be.
Another approach you might want to take would be to layer the inner/negative/inner handle shape underneath the primary/outer/mug shape and do Pathfinder/Minus Back.
Here's an example file
Compound Path and Pathfinder Minus Back
Vince
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