Answer:
There was a major conflict between the Patricians and the Plebeians called Struggle of Orders, while both sides were on a strike Patricians realized that it was too much of a hassle to do all the work of the Plebeians, therefor they allowed a Plebeian consul.
If the government was run of Patricians the lower class, aka.. the Plebeians would not have a say, and the rich upper class would have all the power.
