isn't being resolute of arrogance another way of acchieving something selfish? Since arrogance puts the person in an urge, even if it is not to obtain something, in a way, it is to selfishly change from this ''state of arrogance'' that the person will act.
An act can have the byproduct of benefiting oneself (I.e. feeling you did the right thing) without that product being the motivating driver. E.g. You help an elderly person up who has fallen while crossing the street because you are worried for their safety. After, you feel good for helping.
Considering the statement is talking about an unselfish act, it would have to be completely unselfish for it to contradict this argument. Saving someone is highly rewarding and also lets the person's mind be free of remorse, which definitely makes it benefit the one who does the act.