The reason she gives Parris is not the real reason. She states that she was discharged from the Proctor household because Elizabeth didn't like her and wanted her to be a slave. Although, she didn't say it that nicely. Instead, she vindictively rants,"She hates me uncle, she must, for I would not be her slave. It's a bitter woman, a lying, cold, sniveling woman, and I will not work for such a woman...Goody Proctor is a gossipy liar!"
The real reason that she was discharged is because she was having an affair with John Proctor. Elizabeth found out, and fired her; justified, certainly, but Elizabeth underestimated Abigails wrath. Most of the events in the play, most especially Elizabeth's eventual arrest, can be tied to Abigail's hatred of Elizabeth, and her desire to be with John.
According to Reverend Parris, Elizabeth Proctor has said that "she comes so rarely to the church this year for she will not sit so close to something soiled." It is clear that Elizabeth's bad feelings toward Abigail run deep: she doesn't just dislike her on a personal level; she also finds her to be immoral and unscrupulous. Unable to defend herself with evidence against such a charge, Abigail becomes defensive, and she doesn't ever even acknowledge the fact that it was Elizabeth who dismissed her. Instead, she tells her uncle, "[...] I will not work for such a woman!," implying that it was actually her decision to leave the Proctors' employ.
Parris responds that he thinks it is odd that, in seven months, not another family in the village has called for Abigail's service. She responds to this charge, saying, "They want slaves, not such as I. Let them send to Barbados for that. I will not black my face for any of them!" In other words, she accuses all the goodwives in Salem of wanting a slave, and since she refuses to be one they find her unsuitable. Such a defense is designed to secure her uncle's favor and sympathy. He would not want her to lower herself either, and since he already has personal disagreements with half the village, it is conceivable that he would believe they might treat his niece with a contempt similar to what they show him.
Certainly, as the other commenter stated, the real reason Abigail was dismissed is that she was having an affair with John Proctor, an affair they allude to in their conversation, also in this act.