The establishment of the Roman Republic in 509 BCE after the overthrow of the last Roman king, Tarquin the Proud, was a significant turning point in Roman history. The Romans chose to establish a republic instead of a new monarchy for several reasons.
Firstly, the Roman aristocracy, who were the driving force behind the establishment of the Republic, were wary of giving too much power to a single individual. The Etruscan monarchy had become increasingly oppressive, and the Romans wanted to avoid a situation where they could once again be subjected to the whims of a tyrant.
Secondly, the Romans had a deep-seated belief in the concept of the res publica, or the public good. They believed that the best form of government was one that served the interests of the people as a whole, rather than the interests of a single ruler or a narrow elite. The establishment of the Republic allowed the Romans to create a government that was accountable to the people and that placed the interests of the state above the interests of any one individual.
Thirdly, the Roman Republic was established at a time of great social and economic change in Rome. The city was expanding rapidly, and the old social and political structures were no longer able to cope with the demands of a rapidly changing society. The Republic allowed the Romans to create a new political system that was better able to meet the challenges of this new era.
In summary, the Romans established a republic after the overthrow of their last king because they wanted to avoid a situation where a single individual could wield too much power, they believed in the concept of the res publica, and they needed a new political system that could better meet the demands of a rapidly changing society.