Anne Putman (also referred to as Mrs. Putnam, Goody Putnam, or Goody Ann) has a massive grudge against Becky Nurse because Goody Nurse has 11 children and over 26 grandchildren (albeit, at a relatively young age), and in contrast Mrs. Putnam has had nine children, all of which have died, except for one girl. Now, that one girl, Ruth has what appear to be petit mals, or seizures, and Goody Putnam is very angry that Becky enjoys the pleasures of motherhood while Ann has seen all her children die. As a result, the upcoming witch hunt will bring everyone and their cousin down. Ann takes that opportunity to hint at the fact that Goody Nurse is a witch and for this reason she says the phrase:
You think it God’s work you should never lose a child, nor grandchild either, and bury all but one? There are wheels within wheels in this village! And fire within fires!
This is basically a direct accusation stating that Becky is protected by a supernatural power to not go through the pains and tribulations that Anne has gone trough.
In addition to the reasons mentioned by my esteemed colleagues above, there is also the vindictive nature and greed of the Putnams which one should consider. Anne Putnam is obviously greatly troubled and aggrieved by the failure of her babies to survive beyond their birth, but she has other resentments as well. One should also consider that since it was so easy for her husband, Thomas, to use his daughter, Ruth, as a tool during the trials, he could not have found a more willing partner to his pernicious scheme than his wife.
Arthur Miller, in his notes, refers to the vindictive nature of the Putnams, specifically as it is directed towards the Nurses:
Another suggestion to explain the systematic campaign against Rebecca, and inferentially against Francis, is the land war he fought with his neighbors, one of whom was a Putnam...
... As we have seen, Thomas Putnamn's man for the Salem min-istry was Bayley. The Nurse clan had been in the faction that prevented Bayley's taking office. In addition, certain families allied to the Nurses by blood or friendship, and whose farms were contiguous with the Nurse farm or close to it, combined to break away from the Salem town authority and set up Topsfield, a new and independent entity whose existence was resented by old Salemites. That the guiding hand behind the outcry was Putnam's is indicated by the fact that, as soon as it began, this Topsfield-Nurse-faction absented themselves from church in protest and disbelief. It was Edward and Jonathan Putnam who signed the first complaint against Rebecca; and Thomas Putnam's little daughter was the one who fell into a fit at the hearing and pointed to Rebecca as her attacker. To top it all, Mrs. Putnam - who is now staring at the bewitched child on the bed - soon accused Rebecca's spirit of tempting her to iniquity, a charge that had more truth in it than Mrs. Putnam could know.
It is clear, therefore, that Anne Putnam's resentment was borne not only out of her jealousy with regard to Rebecca's success in raising babies, but also that the Nurses were seen as enemies. Also, with them out of the picture, Thomas could purchase their land at auction once it has been declared forfeit to the state. The Putnams would have killed two birds with one stone.
Miller's ironic concluding note in the above extract asserts that it is Anne Putnam who turned to evil, contrary to her resolute attempts to prove that it was the other way round.
Ann Putnam is a very jealous woman. She holds a grudge against many of the people in Salem. When all of the talk about witchcraft comes to town, she sees her opportunity to accuse one of the people she holds a grudge against the most.
Rebecca Nurse is one of the most respected citizens in Salem. She is kind and has a warm heart. She has been the midwife for Ann for many of her births. Ann has had eight children, and all but one has died at birth. She is angry and jealous. Rebecca Nurse has many children and grandchildren, and Ann is now seeing her chance to make Ann pay. Ann knows that Tituba practices voodoo, so when the hysteria breaks out, she lays the foundations for the accusations of Tituba and Rebecca Nurse.
"Reverend Parris, I have laid seven babies unbaptized in the earth. Believe me, sir, you never saw more hearty babies born. And yet, each would wither in my arms the very night of their birth. I have spoken nothin', but my heart has clamored intimations. And now, this year, my Ruth, my only- I see her turning strange. A secret child she has become this year, and shrivels like a sucking mouth were pullin' on her life too. And so I thought to send her to your Tituba"
Here she is setting up the accusations that she believes that there was a supernatural murder of her babies, and that Rebecca Nurse was behind all of it, using witchcraft.