The reason is 2 fold, so let first define what a republic is by contrasting it with democracy.
A republic is where the people elect other people to make policies, rather than a democracy, where people do governmental policies themselves by themselves.
In essence a republic is a little bit more fair than a democracy, because in a democracy the majority always wins.
So, that’s one of the reasons why the Romans wanted a republic, because it’s more stable and more fair.
Another reason is because of their disdain for the monarchy that once ruled over them; and based on that delicate balancing act of having the aristocrats rule whilst ensuring that none of them would grow powerful.
I hope that helps.
