In accepting gifts from Mephistopheles, engaging in wagers with the devil, and directly challenging the spiritual and ethical standards with which he has been molded to live socially, Faust demonstrates arrogance in the way that he feels that he is above any moral consequence for his actions.
Not only is he arrogant, but he is also greedy, careless, selfish, and narcissistic. All of these are tantamount to arrogance. While a lot of people experience the same things, and may also be arrogant, Faust goes above and beyond by making his particular manifestation of haughtiness entirely official in the eyes of the higher powers; he is essentially saying aloud "look what I can do", and he freely engages in situations and behaviors that are as bad as they are dangerous.
Moreover, Faust believed that he, out of anyone in this universe, would be able to manipulate all the forces that rule the spiritual and moral realm. To add to this shocking conclusion, he also feels that he can test and directly challenge the devil by taunting and mocking him. Faust is really testing his limits, but he really does not seem to care. Added to his arrogance, there is also a sense of entitlement that leads him to feel that he is smarter and better off than those which rule or mold the world.
A spectre this from which all shrink afraid.
The word its life resigneth in the pen,
Leather and wax usurp the mastery then.
Spirits of evil! what dost thou require?
Brass, marble, parchment, paper, dost desire?
Shall I with chisel, pen, or graver write?
Thy choice is free; to me 'tis all the same.
In his view, while he knows for a fact that the devil is evil, and nothing to be making friends with, he is arrogant enough to feel that the devil would spare him, of all people. Yet, Faust questions everyone, criticizes, judges, and opines as if he has the right to do so. Unfortunately for the reader, the novel will not be cathartic, as Part Two will show. Nevertheless, in Part One, we as readers get to meet who Faust really is and we get to understand why he would need a severe punishment at some point in the future.