What is the purpose of making a Yagi’s parasitic elements either longer or shorter than resonance?

A Yagi antenna achieves its directional pattern through the interaction of electromagnetic fields radiated by its driven element and its parasitic elements. To make the signals combine constructively in the forward direction and destructively in the reverse direction, the currents in the parasitic elements must be carefully phased. By making a parasitic element slightly longer than resonance (like a reflector), it becomes inductive, causing the induced current to lag in phase. Conversely, making it slightly shorter (like a director) makes it capacitive, causing the current to lead in phase. Therefore, adjusting the physical lengths of these elements is the primary method used to control the necessary electrical phase shift.