“You made me mad” gives your emotions a remote control and hands it to someone else.

That sentence hands the controls to whoever you are angry at. If they caused the feeling, then only they can end it, and you are stuck waiting for someone else to change. What they did mattered, and the reaction still happened inside you. Owning the reaction is not letting them off, it is keeping the part you can steer.

Swap the phrasing when you are upset: I got angry when that happened. Same event, and you keep the ability to decide what you do about it.