奎 originally depicted a person striding with legs apart. In Chinese astrology, 奎宿 is associated with literature and scholarship - the 奎星 (Kui Star) was worshipped as the patron of examinations.
The top 大 depicts a person with arms outstretched and serves as the indexing radical. In 奎 it sits above 圭, suggesting a striding figure whose legs span a wide gap - the source of the 'wide stride between the thighs' literal meaning.
The bottom 圭 (jade tablet) supplies the sound, giving kuí close to guī with tone shift. 圭 appears as the phonetic in a family of guī/kuí characters (闺, 桂, 蛙); here it pairs with 大 to anchor the lookup and provide pronunciation.
