What does the convexity effect actually mean for equal rate moves?

There is a clean way to think about it. Positive convexity means the bond price-yield line bows outward. Because of that bow, a yield decline lifts the bond price by more than a yield increase of the same size pushes it down.

If you imagine duration as a tangent line at the current yield, the exact bond prices sit above that line on both sides. That creates the asymmetric outcome. It is not memorization for its own sake. It is the geometry of the price-yield curve.