Why does Antony think Lepidus should not rule

with Octavius and him?

Answer: He is not a leader

Explanation: Antony believes that Lepidus should not rule with him and Octavius because to him, Lepidus is only a follower, not a leader. He is not worthy of being part of the triumvirate. Antony only sees Lepidus as the errand boy, not someone worthy of leading with him and Octavius. He even compares him to a horse, which is also only a follower.