Why use contribution margin in AED instead of food-cost percentage?

Because you bank dirhams, not percentages. A dish with a low food-cost percentage can still contribute very little cash per plate, while a higher-percentage dish can be your strongest earner once volume is taken into account. Food-cost percentage is a useful control, but contribution margin in money — menu price minus the plate's ingredient cost — is what actually pays the rent. Use both; let the cash figure decide.

From Menu Engineering: How to Price a Restaurant Menu for Profit — the full reading, with the method behind this answer.