Arrogance

Arrogance is perceived as a negative quality because it is associated with

A lack of courtesy to others.
The possibility that arrogance is a cover for insecurities.
A lack of self-awareness. I could be arrogant because I have a PhD, but everyone I work with does too!
Narcissism. Excessive self-involvement.
A lack of intellectual humility. An arrogant person cannot recognize that s/he may be wrong.

Yet some quality resembling arrogance is also necessary for the following reasons:

Confidence. You have to project a sense of confidence, that you know what you are talking about. Making apologies for oneself or being too self-deprecating can backfire. I remember dumbshit students taking my profession of ignorance about something at face value. I've seen people apologize first, then give a bad presentation. When you say, "I don't have these ideas very well developed yet," and you really don't, then people will be sitting there thinking, "You are right, you don't."
Honesty about one's capabilities and accomplishments. Look at your cv as though it belonged to somebody else. If you are impressed by what you see, then you should be impressed with yourself.
Ambition. It is hard to be ambitious if you are too afraid of being arrogant.

Also, you have to distrust the motives of people who call you arrogant. Are they jealous? Are they trying to hold you back or put you down? When I published in Insula as an Assistant Professor, a senior colleague, instead of congratulating me and encouraging me to take legitimate pride, made a snarky remark about my "swelled head."

So narcissism and rudeness, bad. Ambition, legitimate pride in real accomplishments, good. False humility and apologetic discourse, bad. Intellectual humility about being wrong, good.