短 vs 矮: 短 is for length and duration (short road, short time, short hair). 矮 is for height of people and objects (short person, short building). Never use 短 for a person's height.
Left arrow radical — the indexing radical, depicting a feathered arrow. In ancient times the arrow was the standard short measuring stick (the bow 弓 was the long one), so 矢 anchors 短 in the imagery of measuring brevity. Same radical appears in 知 to know and 矮 short-in-height.
Right side 豆 — a stemmed ritual serving stand (later borrowed for 'bean'). Both an arrow and a serving stand are short objects: 短 is a compound ideograph of two short things side by side. The bean reading is later — the original sense here is the squat vessel.