Why does Proctor confess to lechery?
In Act III Proctor confesses that he "has known" Abigail. This two-word euphemism shatters his image and forces him to own up to his biggest secret. That he has committed adultery- he is a lecher.
He confesses when he runs out of all other options. He has tried to give the courts proof that the girls are lying, but Danforth will not listen. Presented with no other options, he explains to the court why and how he knows that Abigail would want Elizabeth convicted and executed. Because of his actions, she is in love with him and feels that with Elizabeth out of the picture, she might have a chance.
PROCTOR: Whore! How do you dare call Heaven!
DANFORTH: Man! What do you---?
PROCTOR: It is a whore.
ABIGAIL: Mister Danforth, he’s lying!
PROCTOR: Mark her, now she’ll suck a scream to stab me with, but—
DANFORTH: You will prove this, this will not pass.
PROCTOR: I have known her, sir. I have… known her.
DANFORTH: (A pause. His eyes stare incredulously at Proctor.) You… you are a lecher?
NURSE: (Horrified.) John, you cannot…
PROCTOR: No, Francis, it is true, it is true. (Back to Danforth.) She will deny it, but you will believe me, sir; a man… a man will not cast away his good name, sir, you surely know that—
DANFORTH: In what time…? In was place?
PROCTOR: (Hanging head, turning front.) In the proper place—where my beasts are bedded. Eight months now, sir, it is eight months. She used to serve me in my house, sir. A man may think God sleeps, but God sees everything. I know it now. I beg you, sir, I beg you—see her for what she is. My wife, my dear good wife took this girl soon after, sir, and put her out on the high road. And being what she is, a lump of vanity, sir…. (Starts to weep.) Excellency, forgive me, forgive me. She thinks to dance with me on my wife’s grave! And well she might!—for I thought of her softly, God help me, I lusted, and there is a promise in such sweat! But it is a whore’s vengeance, and you must see it; I set myself entirely in your hands, I know you must see it now. My wife is innocent, except she know a whore when she see one.
Proctor's confession is his last resort. With the court blind to the truth and with weak Mary Warren turning on him, his only hope is to delineate the true cracks in Abagail's so called "holy" reputation.