(Natural) marriage is an inherently sexual contract and it is contracted between two parties, male and female, only one of which holds a monopoly on violence. The other party's contractual rights, and the rights of the children born into the contract, have to be defended by a separate male party.
That is why marriage isn't like a business contract, where it's two people making a deal at eye-level, that they can just walk away from and shrug. And this is why marriage is "the" contract, and not merely "a" contract.
It is a contract linking two societies or bloodlines.