Why does Proctor confess to lechery in The Crucible?
Because John Proctor himself disdains hypocrisy, so much that he has even exposed that of others, he is greatly disturbed by the claims of Abigail Williams and the other girls that certain witches in town cast spells upon them. When his wife Elizabeth is among those accused of casting such "fits" upon the girls who were caught frolicking without their clothes in the forest, John feels compelled to defend his wife no matter what the cost is to his own reputation. He, therefore, brings Mary Warren, one of the girls who made the false accusations of witchcraft against the women; Mary admits that she and the others merely faked their fits. However, when the girls are summoned, led by Abigail they deny these charges. So, in a final attempt to defend Elizabeth, his wife, and discredit the vindictive Abigail, John Proctor confesses his sin of adultery committed with Abigail in order to explain her motives in discrediting Elizabeth who has fired her after learning about the affair. He admits to lechery because Abigail is only seventeen and he is a mature man.
A man may think God sleeps, but God sees everything, I know it now. I beg you, sir, I beg you—see her what she is. . . . 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. . . .
In this scene, the climax of Arthur Miller's play, John Proctor realizes that the witch trials are merely Abigail's attempt to avenge herself against him for ending their affair. He has been reluctant to make this confession which sullies his good reputation, but his sense of what is right and his love for his innocent wife supersede his sense of self-preservation. So, he confesses to his sin of lechery in order to save Elizabeth.