The Putnam clan had grievances with many people over many issues. Land is just one of them. A certain grievance they had over land may have indeed led to Rebecca Nurse being named as one of those practicing witchcraft. This was very counter to Rebecca's character. Some narration in Act I reveals:
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 Pitnam. This squabble grew to the proportions of a battle in the woods between partisans of both sides, and it is said to have lasted for two days.
Moments later, readers discover that the Nurses have sold the land in question to John Proctor which creates another grievance between a Putnam and another person.
Putnam: A moment, Mr. Proctor. What lumber is that you're draggin', if I may ask you?
Proctor: My lumber. From out my forest by the riverside.
Putnam: Why, we are surely gone wild this year. What anarchy is this? That tract is in my bounds, it's in my bounds, Mr. Proctor.
Proctor: In your bounds! I bought that from Goody Nurse's husband five months ago.
Putnam: He had no right to sell it. It stands clear in my grandfather's will that all the land between the river and -
This is just the beginning of another problem with land for the Putnams. That particular will that Putnam references caused quite a dispute among the heirs. Putnam did not really receive very much at all from his grandfather and he took family to court to try to get a greater share.
Putnam seems to regularly be outside of what is fair and just and believes he deserves more than he receives. Perhaps he was just not a well liked person.