By the time we reach act 4 of The Crucible, it's clear to many people in Salem, including Reverend Hale, that the witch trials are built on lies and false testimony. But the outbreak of mass hysteria that has this small Massachusetts town in its viselike grip has taken on a terrible momentum all of its own, so much so that it's become almost impossible to stop.
Even Deputy Governor Danforth seems to realize that there's no truth to any of the accusations of witchcraft that have been floating about the town. That would most probably explain why he gives John Proctor, Rebecca Nurse, and Martha Corey the chance to save themselves from the gallows if only they'd confess to the charges of witchcraft leveled against them.
But none of these prisoners is prepared to admit to these wholly false charges. This prompts Reverend Hale to intercede with Danforth to obtain pardons for them. However, Danforth won't accede to Hale's request. Granting these prisoners a pardon would be like admitting that they're innocent, and that would undermine the integrity of the witch trials, not to mention Danforth's credibility as a judge. There will be no pardons, then, and so the prisoners must hang.