Final answer:
Romulus and Remus both believed they should be king due to their royal lineage and having overthrown their treacherous great-uncle. The dispute was resolved when Romulus killed Remus, leaving Romulus to found Rome and establish its monarchy, which lasted until the republic was founded to avoid tyranny.
Step-by-step explanation:
Both Romulus and Remus laid claim to the right to be king as they were direct descendants of a Latin king, restored their grandfather to the throne, and led the founding of Rome after being suckled by a she-wolf as infants. This narrative was central to Rome's legendary founding, a story that highlights the Roman values of force, power, and legitimacy.
The conflict between the brothers was decided in a tragic manner when Romulus killed Remus amidst a dispute over where to found the new city and who should rule it, an act which not only left Romulus as the sole ruler but also as the namesake of Rome.
According to Roman mythology and tradition, the founding of Rome and the establishment of its monarchical rule began with Romulus. The king ruled until the Romans disposed of the last king, Tarquinius Superbus, establishing a republic to avoid the feared tyranny of a monarch. This shift from monarchical rule to a republic demonstrated the Roman commitment to the rule of law and their dedication to preventing any individual from gaining excessive power.