In "The Crucible" why did Arthur Miller incorporate Abigail in the story the way he did? What are examples of her bitterness?

Abigail Williams adds drama, suspense, intrigue, and tons of motive for all of the accusations that occur.  In the real Salem Witch trials, she was only eleven, and John Proctor was in his sixties, and there was no affair that occurred at all.  So, Miller tweaks things a bit in order to add drama to the play itself.  Interestingly, his added and fictional affair makes the accusations much more understandable and less illogical than they were in real life.

Not only did Abby's character drive most of the accusations that occurred in the play, she also expressed bitterness and resentment over several different things.  A lot of this bitterness can be found in the opening pages of the play itself.  One thing that she is bitter about is the fact that people are gossiping about her in the town, and claiming that her reputation is tarnished.  Parris questions her about her reputation, and she lashes back, arguing, "There be no blush about my name!"  She is resentful that anyone would say bad things about her, and expresses a lot of bitterness over the fact that she is the subject of gossip.

Another thing that she is bitter about is how she is expected to be a servant in other people's houses.  Abby is not one that takes kindly to being told what to do, and resented it in the Proctor household, and resents that no one else will hire her after she is fired.  She says, "They want slaves, not such as I."  She hated being bossed around, and doesn't like the fact that she is expected to be a servant to get by.  She is also bitter that she has to live in her uncle's house, and that she is beholden to his kindness; she asks, "Do you begrudge my bed, uncle?"  She is asking if he is upset over the fact that he has to take care of her and house her.  She resents being beholden to him.

One last thing that Abby is bitter about is how everyone in Salem acts super righteous, when deep down they all harbored bad desires and habits themselves.  In talking to John, she mentions how he opened her eyes to "what pretense Salem was."

As a whole, Abby's a pretty bitter person about a lot of things.  Miller paints her as a resentful, hateful person, who is bent on getting what she wants, no matter the cost, and that makes for a really good antagonist.  I hope that those thoughts helped; good luck!