A good example, Susan! Let's try an older show--The 'A' Team. Four men, all Alphas in their own right. Not a beta among them, but with VERY different personalities. They had different ways to express themselves . . . and applied them equally to men and women.
Hannibal -- like Jack of SG, he's the "leader" of the group. He lets his people handle their specialties, but you get hints and bits that he's every bit as competent to TAKE OVER their job if it came down to it and one was disabled. He DEMANDS the best from his people and won't coddle them. Sometimes he's closer to Gordon Ramsey of Hell's Kitchen. "It's just a cut. Doesn't even need stitches. Quit whining and get back to work!" Does that make him arrogant (or Gordon, for that matter?)
Face -- The "playboy", but great to have at your side in the clutch. He's warmer and fuzzier than Hannibal and is happy to seduce any woman who comes within a country mile. He'd rather not confront people, but CAN if required. He's INCREDIBLY arrogant, to the extent that he truly BELIEVES people are there for his own personal use. He manipulates them freely--will lie, cheat or conk them on the head and steal for his goal. But if the goal is HONORABLE, does that make a difference? Is a reader willing to go along for the ride . . . let him manipulate, so long as they understand the goal?
Murdock -- The "wild and crazy" one. He's borderline psychotic, but will die for you without hesitation. But he'll also drive you over the edge with smart-a$$ remarks, and a quick temper. If the mood strikes him, he'll just as easily put a person in tears or leave them screaming in pain. Is THAT arrogant?
BA -- The "strong, silent" one. Prone to anger, he's never hesitated in hitting things and people. But he's a softy for the underdog, willing to stop a firefight to pull a puppy from the field. But he yells and screams at people--intending them to be emotionally hurt. How about that?
This is why it can be frustrating to a writer, trying to pick something and make it believable.
So, what say you all? Are ANY of these arrogant? Have you written/would you write a character like one of these?