This squabble between the Putnams and the Nurses has deep roots. You can find great quotes about this issue because there are several of them in Act I when Rebecca Nurse is introduced. Miller takes the opportunity to diverge from dialogue and gives some background in prose:
Francis Nurse... was called upon to arbitrate disputes as though he were an unofficial judge. By the time of the delusion, they had three hundred acres.
No one seems to account for how he got this land. Although generally, he was a well-respected man people would trust.
Another suggestion to explain the systematic sampaign against Rebecca, and inferentially against Francis, is the land war he fought with his neighbors, one of whom was a Putnam.
Yet another suggestion from Miller's text explains the sides that Salemites took in the positioning of a new minister:
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 Salem town authority and set up Topfield, a new and independent entity whose existence was resented by old Salemites.
The text goes on to assert that Putnam was likely one of those and Putnams signed the first complaints against Rebecca Nurse regarding witchcraft... coincidentally.
This grudge lead to corruption because these claims and complaints of the Putnams encouraged the young girls who further claimed others with the Nurses had been seen with the Devil. These people eventually hung after false accusations.