The parallel-axis theorem adds Md²
The mistake
Adding Md or shifting moment of inertia by a linear distance.
Why it feels right
The axis moved by distance d, so a linear correction feels natural.
How to catch it
Your corrected moment of inertia has units kg·m instead of kg·m².
The first principle
For a parallel axis a distance d from the center-of-mass axis, I = I_cm + Md².
worked mini-example
A disk has I_cm = ½MR². What is I about a tangent axis parallel to the central axis?
Common wrong move
I = I_cm + MR.
Correct
I = ½MR² + MR² = 3MR²/2.
Test the repair ROT-10 · transfer
Make a fresh prediction before referring to the worked example.