His arrogance is deflecting from feelings of inferiority. No confident smart person would ever refer to themselves as a "genius."
I've got a pretty foolproof test. Tell someone during a conversation "you're a smart guy/woman."
A genuinely intelligent person, or even most averagely clever people, will look a bit sheepish or embarrassed. Disbelieving even. Some intelligent confident people will ignore it.
A dummy will, without fail, beam with delight. You see their chest puff up and their eyes shine. Finally, someone has recognised their genius!