As the first answer states, I don't think that you can argue logically from Miller's play that John Proctor is responsible for the witch trials. Miller makes it quite clear that religious hypocrisy, obsession with power, and greed for land are to blame for the trials.
That being said, in addition to the first post's points, you could argue that John's pride--demonstrated by his unwillingness to expose Abigail when she first tells him that the girls were faking or his refusal to listen to his wife because he is bitter toward her--causes the trials to escalate.
One more point, if John had not establish a rather ungodly reputation (in the Puritans' eyes) by working on Sundays and not attending church regularly, he might have carried more veracity in the community early on when he speaks out against bringing Hale to town.
I am not at all sure I agree with the statement, but here's how I would answer it if I had to.
First, he causes the trials by having an affair with Abigail. It is partly her anger at Elizabeth Proctor (and maybe at John) that causes her to start lashing out.
Second, he probably helps make Hale suspicious by the ways in which he answers the questions that Hale asks when he visits the Proctors. Hale probably believes that it is important that Proctor doesn't know all ten commandments.
Finally, you could say he made the authorities even more suspicious because of how he behaves when they come to arrest Elizabeth.