Elizabeth Procter actually reveals the best information that we get about this question.  John Proctor never explains why he does this other than revealing that he did once lust for Abigail and stating that his wife was sick.  However, in the end of the play – Act 4 – when Elizabeth is asked to get John to confess, she does blame the entire affair on herself.  She says, “It were a cold house I kept.”  Basically, she is telling him that he should not blame himself for what he has done because she was a very cold, unloving person toward her husband; she seems to feel that she drove her husband away from her and toward the only other woman who lived in their home – Abigail.

In the final act, when John and Elizabeth are talking, she alludes to some possible issues that had prompted the affair.  She says, "I have sins of my own to count.  It needs a cold wife to prompt lechery", perhaps referring to the fact that she was a stern, unkind woman, who was not very loving to John.  She admits that "I never knew how I should say my love. It were a cold house I kept."  So, she was not very openly loving, and had a hard time expressing her love for John.  This, in combination with the fact that she had been "a long time sick", might have driven John away from her into Abby's arms.  It doesn't justify the act, but at least gives us a clue as to some of the reasons why it happened.  

We can't leave out the Abby factor though.  If nothing else, this play shows her fierce determination when getting something that she wants.  She wants John so badly for herself that she shoves a needle into her own belly to set Elizabeth up.  Who knows what sort of scheming she did in the actual household when she worked there, in order to tweak situations into her favor.  All in all, the affair was highly unfortunate, and leads to some very disasterous situations.

Why did John Proctor disclose his affair with Abigail?

By this stage in the play John's getting pretty desperate. The way things are going both he and his wife Elizabeth are heading for the gallows. So John somehow has to undermine Abigail's credibility as an accuser. Getting Mary Warren to spill the beans didn't work so he openly admits to having had an affair with Abby.

John's confession is supposed to provide the court with a rationale for Abby's making all these false accusations. She's a scorned woman who wants revenge. In Puritan communities at that time there was a double standard when it came to adultery. Although it takes two to tango, as it were, the woman involved was always blamed for any affair, and would be labelled a "scarlet woman," or a "temptress." John knows this, which is why he reveals the affair.

Unfortunately for John, his gameplay fails miserably. Elizabeth, thinking that she's protecting her husband's...

Why did John Proctor disclose his affair with Abigail?