When you really believe in something with all your heart and would do anything to stand your ground, you can come off as arrogant, even though that is the last thing your want to be.
There is indeed a fine line between confidence and arrogance.
This is what I have observed:
One will listen to you and ask you questions to let you have your own opinion. The other will just insist he is right.
One will genuinely appreciate your accomplishments even though you both know you are not in his league. The other will put down or dismiss what you have done.
One respects those he does not agree with. The other bad mouths them especially behind their back.
One is humble. The other is proud.
What other behaviors have you seen?