Genesis 2:24 directs a couple to cleave to each other in order to become one flesh. The meaning of "cleave" is to glue together. The process begins by them choosing to be together, promising that they will fulfill the covenant, and trusting that each will do his best. They will then function as one. God, also, is at work in this joining process as "a cord of three strands is not quickly torn apart" (Ecc 4:12).
It is worth considering whether being "one flesh" is literal or figurative. "The wife does not have authority over her own body, but the husband does; and likewise also the husband" (1Co 7:4). It is a matter of ownership. "You are not your own" (6:19). "You have been bought with a price" (:20). Closeness and interdependence bonds a marriage together. There is the "natural use of the woman (Romans 1:27)" which synergistically makes the two one flesh. This is brought out in an unusual way. 1 Corinthians 6:16 says sexual relations with a prostitute joins them in one body. Even though there is a connotation of one literal body it makes more sense to regard it as figuratively representing a commitment between two people which brings them closely together. So when "one flesh" is used in Genesis and the Gospels it is a figure of speech denoting oneness.
Both Jesus and Paul quoted "a man shall leave his father and mother, and be joined to his wife; and they shall become one flesh" (Gen 2:24). But we just saw that joining with a prostitute unifies their bodies. How can becoming one body be put in the same class as becoming one flesh? Perhaps an alternate definition applies to Paul’s use. Nevertheless, we do get an insight from this dichotomy. Matthew identifies it. In verse 5:32 he says that unfaithfulness is grounds for a valid divorce. A husband (or wife) joining in one body with a person they’re not married to causes the one flesh union to be broken. That shows how important the physical union is. It is a reflection of the state of the other ingredients in the marriage. Divorcing someone itself would be equivalent to the physical violation. So if the Exception Clause enables a person to extradite himself, why wouldn’t a divorce by the other person free the innocent party from culpability as well?