why would proctor admit, but not sign a confession of his guilt?

Proctor is a man searching for some moral self-respect. His affair with Abigail has been beating at his conscience since the play began. Finally at the end, stripped of his integrity, Proctor is given a chance to save himself and his wife from execution. All he has to do is confess that he hangs out with the Devil. This seems like an easy thing to do. Rev. Hale points out that all Proctor needs to do is sign his name to give the witch-court validation which will keep them in business. Proctor, however, decides that his name is all he has. John is a man of integrity or rather a man that desperately seeks integrity. A verbal confession under extreme duress is one thing but the physical writing of his name represents who he is as a man. Proctor can not sign the confession. To sign it would be the tangible and final loss of his integrity. He aptly sums this up when he cries out, "All I have is my name!"

Its because he knew that if the confession was nailed to the church with his signature he would lose the value of his name. His name's reputation and the future of his family would forever be 'scarred'.