> Because it's the state using it's monopoly on violence
Divorce is itself an instance of the state’s “monopoly on violence”. A state agent (a judge) will decide on issues such as property and custody, and then the state’s “monopoly on violence” will be used to enforce that judicial decision. “At gunpoint” even. Or else, the parties may reach an agreement, a settlement - coerced by the threat of a judge deciding it if they don’t - and then the “state’s monopoly on violence” will be used to enforce that agreement, and in particular the state’s interpretation of it.
Frequently, divorce is forced by the state’s threat of violence on an unwilling spouse. I saw with my own adolescent eyes how my mother used the state’s monopoly of violence to force divorce on my father even when he didn’t want it, and when he was the victim of her adultery-a fact about which the state chose not to care. My father was the victim-and I believe that my siblings and I are victims of her adultery too-my mother the perpetrator-and the state used its monopoly of violence to help her in victimising us. And while I never saw a gun in the whole sorry saga, state agents with guns were only ever a phone call away.