Romulus allowed the husband to repudiate his wife if she had committed an adultery, prepared poison, or counterfeited the keys. He did not give wives the right to repudiate their husbands. Plutarch calls this a very harsh law. 
As the law of Athens gave the option of repudiation to the wife as well as the husband,  and as we see that women obtained this right among the early Romans despite the law of Romulus, it is clear that this institution was one of those which the deputies of Rome brought back from Athens, and that it was included in the law of the Twelve Tables.
Cicero says that the causes for repudiation came from the law of the Twelve Tables.  We thus cannot doubt that this law had increased the number of causes for repudiation established by Romulus.
The possibility of divorce was again a provision, or at least a consequence, of the law of the Twelve Tables. For from the moment the wife or the husband had separately the right of repudiation, they could a fortiori agree to separate by mutual consent.
The law did not require people to give causes for divorces.  For by the nature of the thing, there must be causes for repudiation, and none is required for divorce because wherever the law establishes causes that can break up a marriage, mutual incompatibility is the strongest of all.
It is reported by Dionysius of Halicarnassus,  Valerius Maximus,  and Aulus Gellius,  that even though the option of repudiating one’s wife was available in Rome, there was such respect for the auspices that no one for five hundred twenty years  availed himself of this right until Carvilius Ruga repudiated his wife for cause of barrenness. I do not find this convincing. You only have to know the nature of the human mind to appreciate what a marvel it would be if, when the law granted such a right to a whole people, no one availed himself of it. Coriolanus, departing in exile, advised his wife to marry a happier man than he.  We have just seen that the law of the Twelve Tables and the Roman ethos greatly extended the law of Romulus. Why these extensions, if no use had ever been made of the option to repudiate ? Further, if the citizens never repudiated because they had such respect for the auspices, why did the legislators of Rome have less ? How did the law constantly corrupt the ethos ?
By comparing two passages in Plutarch we shall see the wonder of this matter disappear. The royal law allowed repudiation by the husband in the three cases we have mentioned.  “And in other cases,” says Plutarch, “it held that he who repudiated be required to give half of his possessions to his wife, with the other half being devoted to Ceres.”  Thus repudiation was possible in every case by submitting to the penalty. No one did that until Carvilius Ruga,  who, as Plutarch further says, “repudiated his wife for cause of barreness, two hundred thirty years after Romulus.”  In other words, he repudiated her seventy-one years before the law of the Twelve Tables, which extended the power to repudiate and the causes for repudiation.
The authors I have cited say that Carvilius Ruga loved his wife, but that the censors because of her barrenness made him swear he would repudiate her so he could give children to the republic, and this made him repulsive to the people. You have to know the genius of the Roman people to discover the true cause of the wrath they conceived for Carvilius. It is not for repudiating his wife that Carvilius fell from favor with the people ; that was something that did not concern the people. But Carvilius had sworn to the censors that, given his wife’s barrenness, he would repudiate her so as to give children to the republic. That was a yoke which, as the people could see, the censors were going to put on them. I shall make clear later in this work  the aversion they always had for such requirements. Laws must be explained by laws, and history by history.