The answer to this question can be found in the extra information that Miller provides about the character of Putnam when we first meet him in Act One, and in particular, his grasping, vindictive nature that is so centred on his own personal betterment and enrichment. Consider what we are told about the past incident of Putnam and Burroughs:
Another former Salem minister, George Burroughs, had had to borrow money to pay for his wife's funeral, and, since the parish was remiss in his salary, he was soon bankrupt. Thomas and his brother John and Burroughs jailed for the debts the man did not owe. The incident is important only in that Burroughs succeeded in becoming minister where Bayley, Thomas Putnam's brother-in-law, had been rejected; the motif of resentment is clear here.
Thus the narrative of how Burroughs was wrongfully persecuted by Putnam because of the way that Putnam had felt slighted because his brother-in-law did not get the position that he had wanted him to receive prepares us for the way in which Putnam looks upon the witch trials as a curious way to get revenge against other perceived slights he believed himself to have suffered and to better his own position.