Proctor feels compelled to retract his confession because he admits that people more innocent and closer to God are going to be hung. Particularly, Rebecca Nurse, who is an icon of virtue in the community. She is scheduled to die with Proctor.
Also, there is a practice that when someone confesses to witchcraft, their land is confiscated and sold at a discounted price. So if Proctor goes ahead with his confession, being pressured by Danforth and Parris to sign his name to a written confession to be hung on the church door, he will lose his property and soil his name, not only for him, but for his sons.
Proctor cries, "It is my name," he will only have one in his life, therefore, in order to bring dignity and honor to the Proctor name John must retract his confession. He can't bear the thought of living with a name that has been disrespected. Since he confessed to the adultery with Abigail, Proctor feels like he is right with God. He does not want to risk his immortal soul at this point. His wife, Elizabeth, agrees.