Marriage was invented not just as a contract between a man and a woman. It was also a contract between those two people and any children that would result from the couple's union. Also, it was a contract between that family and society. A major concern was "property rights" and the "right of inheritance."

Back before we had DNA testing that could establish paternity, marriage was a way of demonstrating fatherhood. (Who the mother was is pretty obvious.) In getting married, a man was pledging to recognize as his, any children born by the woman he married. Society was also pledging to recognize that. Traditionally, the law recognized all children born of a particular woman to have been fathered by her husband. People have long understood that's not a guarantee, which is one reason why adultery by a woman was considered such a betrayal of her husband. In ancient biblical times, men had children by their wives, but also by their slaves. The children born of slaves did not have the same rights as the children born of a wife. If a female slave was not Jewish, her child fathered by a Jewish master was not considered Jewish. The Jewish father did not have the same obligations to children he fathered through non-jewish women (usually slaves) as he had to his Jewish children (born of a Jewish mother.)

Most societies did not give children born "out of wedlock" the same inheritance standing as children who were seen as the product of a marital union. In most countries that had a monarchy, only "legitimate children" could inherit the throne (and all that went with that.) Elizabeth the First became queen of England, even though she had an older brother, Henry FitzRoy. He couldn't become king because his father, King Henry the Eighth, hadn't been married to his mother.

When you dig down, a lot of laws and social conventions are motivated by the need to establish "who gets what."