Varys tells the small council that Daenerys is pregnant (which he knows thanks to his spy, Ser Jorah). Robert and the other councillors want to assassinate Daenerys and Viserys, but Barristan Selmy and Eddard vote against that plan.
Eddard feels so strongly that he insults the king and resigns the office of Hand. Whoa!
He prepares to leave the city (and we're totally behind him); but Petyr comes to tell him that he's found another of Jon Arryn's clues: Arryn and Stannis visited a brothel and Petyr will take Eddard there if he stays a little longer in the city. (How will he explain that to his wife? "I was going to leave, but I just had to visit one more brothel…")