Understand them:

When you find your co-worker or your boss is more ego-centric, it is better to understand them more. Do a little research about their behavior as it can help to know where this arrogance comes from. People do often make others look inferior if they have low self-esteem. Those people will be mostly insecure and the ones who want to feel superior in front of others. They will make you feel small and treat you badly; even there is no fault from you.

Take an action:

If the situation goes worst, it is better to take some positive action as possible. Try to impress them with the skills you have, when you prove you can do better than him/her eventually they stop their egotistic attempts to make you feel small. But if you lean to accept situations as it is, it will be affecting both your health and work.