Ego is "I". Arrogant is "I am right". It's one and the same thing. Ego gives birth to arrogance. Ego is the root, arrogance is the fruit.
When you need massage of your ego, you are dependent on your identity. It means a lot to you. You need to assert it. When you start losing your identity, you enter into an identity crisis. You feel insecure. You assert yourself. You need your identity back. You become arrogant.
Ego is a dangerous fruit on which many poisonous fruits grow. Arrogance is one of them. When the ego is watered and buttered, the fruit of arrogance will strike you with disease.
Ego is arrogant !