驳 is often used in compound verbs: 反驳 (fǎnbó, 'to refute/retort'), 驳斥 (bóchì, 'to rebuke'), and 驳倒 (bódǎo, 'to defeat in argument'). Standalone 驳 is more formal.
Left horse radical — the indexing radical. Pictograph of a horse with mane and legs (simplified from 馬). Originally 驳 named a piebald, mottle-coated horse; the 'mixed colors' meaning generalized to 'mixed-up arguments,' then specialized into 'refute, contradict' — countering opposing claims. Family: 骑 ride, 骄 proud, 骏 fine horse.
Right 爻 — two crossed strokes stacked, originally the divination lines of the Yijing. Here the criss-cross pattern visually represents the dappled, intermixed coat of a piebald horse. That mixed/spotted imagery extended figuratively to mixed arguments and contradiction. Same component appears in 爽 bright, 希 rare.