Many leaders got there by force of will, stomping on others, and so on. Your description of yours is not unusual. They generate misery, stress a loathing, none of which serve them, nor their company, nor the working environment.
The question is, what can be done about it?
Their position of power makes things difficult, and their arrogance means some tools, like reasoning, are not going to work as well. But there are things you can do. Because I don't know your details, I can't give specifics, but here are some ideas I've found to be very effective with other clients in similar situations to yours.
- Goal Congruence. Fully understand what your leaders goals are and align what you do with them. In your discussions with them, speak in terms of their goals and how what you're contributing furthers those goals. This should get through the thickest of skins and tell them you're an asset they'll want to treat well.
- Ask Questions - don't defend. Arrogant leaders often like to give orders, to be on the attack. If you can find thinking space (more on that next) break their pattern by asking relevant questions, especially in response to criticism. If they tell you you've done poorly, you might ask them which element of your performance doesn't suit them, or how specifically, you should have been different. Be ready to hear a genuine reason and to learn that you have room to improve, but if you hear different, ask more questions.
- Reduce Stress by stating healthy (exercise, diet and meditation) and by using a part of yourself to step outside and observe the unfolding scene from above. You might narrate "he's doing this, and I'm feeling that". This distancing has a miraculous effect on staying calm and effective under fire. There's always the old "imagine them naked" trick, too.
- Use Body Language to encourage the best behaviour from them. Maintain eye contact during attack; looking down and away is a subordinate gesture. Face them directly. Don't fold your arms or cross your legs. Use pauses with eye contact.
- Use voice tone to manage anger. Don't escalate in pitch or volume or speed, but stay low and slow.