At first, John Proctor shows himself willing to sign a document confessing to witchcraft. He's completely innocent of any such crime, of course; he simply wants to save his life. But when he learns that his written confession will be nailed to the church door for all to see, he relents and angrily tears up the document.
John knows full well what this fateful decision means. He will go to the gallows as a witch, the latest in a long and growing list of innocent victims of the outbreak of mass hysteria that has the town of Salem in its vicelike grip. But John figures that it's better to die with honor than to live in shame and infamy.
In making the ultimate sacrifice, John is protecting his good name. The last thing he wants is for the name of Proctor to become associated in the popular mind with a confession of witchcraft and all the shame and ignominy that that entails. In tearing up his signed confession, John is protecting the good name of not just his present family but that of his descendants as well.
John will soon die, but his name will live on, and it is incredibly important that that name will be forever associated with a good Christian man who did the right thing and not someone who confessed to being a witch.