Mr. Thomas Putnam is a man with a grudge who takes whatever opportunities he can to satisfy his resentment against members of his community for the defeat of his brother-in-law as a candidate for the Salem ministry.
Because his brother-in-law James Bayley was defeated by George Burroughs who was, then, appointed to the ministry in Salem, the vindictive Putnam and his brother later have Burroughs unjustly jailed for debts. In fact, many accusations against citizens of Salem are written in the handwriting of Thomas Putnam. Further, Putnam also has resentment against the villagers who have disregarded him as an intellectual superior; therefore, he is motivated to become involved with any investigation of the residents of Salem. He talks with Parris:
PUTNAM: There are hurtful, vengeful spirits layin' hands on these children.
PARRIS: But, Thomas, you cannot---....
PUTNAM: ....There is a murdering witch among us, bound to keep herself in the dark....Let your names make of it what they will, you cannot blink [close your eyes to] it more.
An opportunist, Putnam may think that an investigation into possible witchcraft under the supervision of the Reverend Hale, who is known for his more scientific approach to things, will serve to possibly cast aspersions against the pretentious Parris, who is a fire and brimstone preacher. Since his daughter and niece are suspected of aberrant behavior, actions that are in opposition to the Reverend's fire and brimstone sermons, Parris's credibility as a religious leader will come into question and Putnam can wreak some revenge against the Reverend.
Certainly, Putnam fuels the fires against Parris as Hale looks at Parris's daughter as in this passage:
PARRIS: Will you look at my daughter, sir?....we discovered her...waving her arms as though she'd fly.
HALE: narrowing his eyes: Tries to fly.
PUTNAM: She cannot bear to hear the Lord's name, Mr. Hale; that a sure sign of witchcraft afloat.