Why would it be wrong to call the Roman republic a democratic system

The Roman Republic ... Once free, the Romans established a republic, a government in which citizens elected representatives to rule on their behalf. A republic is quite different from a democracy, in which every citizen is expected to play an active role in governing the state.

Only the higher class citizens could truly choose who was selected to the government. Slaves and the lower classes didn't get a vote and could not participate in government actions. Democracy is when every citizen, no matter their status in the country, can vote and have a say in how the government is run.