WARNING: The following contains spoilers for The Joker #5 by Matthew Rosenberg, James Tynion IV, Francesco Francavilla, Tom Napolitano, on sale now.
Shortly after the Joker first appeared in Gotham City, he was placed in Arkham Asylum, with his insanity preventing him from being tried before a jury. But Commissioner Gordon was not certain that the then normal mental health facility was properly equipped to contain someone like the mad clown. Gordon then paid a visit to Arkham to keep an eye on the situation, and in doing so made a passing comment that would later ruin his life: he told the Joker that he had children, giving the madman a target and potentially seeding the idea for the tragic events of The Killing Joke.
Jim had every reason to be afraid. He had seen criminals before, but the first time he went up against the Joker he knew that he was different. There was a deviousness to him that made him almost impossible to predict, but Jim was certain that if given the opportunity the madman would break out of Arkham. To alleviate his fears he traveled to Arkham, trying to persuade its staff to move Joker to a more secure wing. He failed, but his belief that Arkham was unprepared for the Clown Prince proved correct when a riot was instigated among the normally docile residents.
Jim found Joker eating a slice of pie, apparently content to watch the chaos unfold around him. Knowing that leaving him out of his cell was dangerous, Jim began moving him back to confinement. But when the mad criminal made a joke about Jim not being able to stop thinking about him, the lawman responded in the worst way. He made a sarcastic remark in which he mentioned that he had children.
The Joker immediately picked up on this fact. He began asking questions about how many he had and how old they were, even making the ominous statement that he loved children. Jim wisely chose to not continue the conversation with the madman, but the damage had already been done. With one sentence, Gordon made his children, Barbara and James Jr., targets that gave the Joker a weakness to exploit.
Although Gordon understood that the Joker was dangerous, at this stage of his career Jim was still used to ordinary criminals. At this time, he didn't fully comprehend the monster that had come to Gotham. All he saw was a particularly twisted criminal who would kill again if given the chance. He had no way of knowing how deep the villain's depravity ran. Joker's first night in Arkham turned out to be an opportunity to understand a little bit about one of the men who he would come to see as an enemy in years to come, and Gordon would pay dearly for his carelessness.
The Joker has always had particular skill in exploiting the flaws and weaknesses of others. It usually manifests in toying with the Dark Knight and trying to get him to break by applying pressure, but Batman isn't an easy target. It takes time and effort to properly hurt him. But Jim Gordon proved to be a much easier target. He openly fights crime, makes a name for himself as one of Gotham's most valiant protectors, and was careless enough to tell Joker about his greatest vulnerability.
Gordon's mistake possibly ruined his entire life. Jim has actively admitted that he still bears mental scars from the night the Joker tried to break him. And his daughter will always bear the scars from that night in a more literal sense. While the Joker probably could've learned this information through other means, this cruel twist likely gives Gordon at least some partial sense of responsibility for putting his family in harm's way.