The answer to this question can be found in the information that Miller gives us about Thomas Putnam and his character, and what drives him as a person. This can be found in Act I and comes just after Putnam enters the room where Betty lies in a catatonic state and Putnam leaps to the conclusion that witchcraft is responsible. The reasons for his resentment and jealousy of others are as follows.
Firstly, his wife's brother-in-law, James Bayley, had tried to become the minister of Salem but was turned down by a faction, in spite of possessing all the qualifications and skills necessary to do the job very well. Putnam's vindictive nature is shown in his treatment of the minister who did get the job, Burroughs.
We are also told that another reason for his jealousy and bitterness stems from the fact that his father left a large proportion of his wealth to his stepbrother. Putnam tried and failed to challenge this.
Note how Miller concludes this section on Putnam's character, commenting on his key role in the denunciations:
So it is not surprising to find that so many accusations against people are in the handwriting of Thomas Putnam, or that his name is so often found as a witness corroborating the supernatural testimony, or that his daughter led the crying-out at the most opportune junctures of the trials...
Thomas Putnam is thus presented as a character who is consumed by both jealousy and resentment, and acts accordingly.