Bill McNabb is CEO of Vanguard, which promotes gender diversity internally and at companies they own shares in. I thought the rationale he described was eloquent and applicable in general. Three points stood out.
First, the goal is corporate performance. Diversity provides material value.
Second, the probability of having all effective leaders in a group partitioned by gender is lower than in an unpartitioned group.
Third, research findings (example) support the hypothesis that a diverse board yields higher performance.