Considering Gen 2:24 from a cultural perspective - meaning the suspected culture in the place and time of Genesis being written - the family unit is patriarchal in nature. The man leaves the protection of his family home and, in turn, becomes the protector of the woman. Although the two never leave from being under God's protection the woman's protection shifts from her birth father to her husband. I'm not sure I like using the word protection here but I'm not sure how to broaden/narrow it. I think it is interesting to notice that there is an equality tacitly entwined, not a master/slave, and this two being one flesh is established prior to any mention of the woman being the child-bearer.
For an easy to read introduction to the patriarchal nature in Genesis, refer to: Arnold and Beyer, Encountering the Old Testament, Baker Academic, 2015, Chapter 5, pages 64-65.