I think the line that draws the limit between arrogance/cockiness and confidence is the ability to prove one's point. For example, a doctor who speaks confidently about plastic surgery is not going to look arrogant, because he's managed to prove he's qualified and experienced. If however, someone starts talking politics very fiercely and proves themselves misinformed, then they will look arrogant. We don't like arrogant people because they indirectly disrespect real skill, knowledge and talent and attempt to fake those.