Seeing Jason as he was back then though, would have overwhelmed Batman with guilt and shame, perhaps even convincing him to retire as a hero entirely. This in turn showcases that Batman prioritized his own needs over Jason's. He knew that he could have helped his son, but he chose not to because it was easier.
Jason Todd was a street orphan until he met Batman after he had saved him from The Joker. Jason was trained by Batman and later became the second Robin, but he was beaten and tortured by the Joker, who sent Batman a video of the event and lied by telling him that Jason was dead.
It will never stop with the Joker
Another thing that Batman knows is that killing the Joker won't ever stop the killings in Gotham. He knows there will always be criminals ready to step up and take the Joker's spot if he gets killed. As such, Batman knows that killing Joker won't do much to rid the city of crime.
On Earth- 51, Batman went on to kill the Joker after Jason Todd's death and eventually killed off a majority of his world's Supervillains in ways that looked like accidents. Because he was never caught, he simply went into semi retirement along with the majority of his world's heroes.
Tl;dr Batman struggled and arguably failed to cope with Jason's death by compartmentalizing it, growing more brutal as Batman, and isolating himself (or rather, failing to maintain relationships or move to heal existing issues between him and other members of the Batfamily like Dick).
He does so not as Jason Todd but as Red Hood… ironically the name the Joker once went by. Batman explains to him that he has a “no-kill” code of ethics and therefore he couldn't avenge his death.
He knew Jason was killing people, and Batman couldn't live with the shame of knowing that he had unintentionally created a deadlier version of Joe Chill. This explains the tragedy of what kept Batman away but also highlights his own selfishness and irresponsibility.
In Arkham Knight, he is kidnapped and tortured for years but not killed. Instead he is mentally abused and made to believe Batman is the source of his suffering. In Arkham Knight, he is starved and beaten, by Joker and by others sometimes dressed up as Batman.
Joker faked Jason's death & sent it to Batman, ensuring that Batman would never try and find Jason. Then, he kept him in Arkham Asylum and tortured him for almost 2 years.
Despite all of their differences later in life, Jason didn't forget about fixing Bruce's father's watch. While he didn't feel comfortable giving the gift to Bruce face-to-face, the fact Jason gave it to him years later shows that he still cares and kept his promise from when he was a kid.
Batman would also feel the same if Joker were taken down while trying to kill others. If he were killed out of revenge, Batman would feel an obligation to bring the killer in, though it might not be popular among the general population.
According to director Matt Reeves, he was born that way. "It's like Phantom of the Opera," Reeves explained to Variety. "He has a congenital disease where he can't stop smiling and it's horrific. His face is half-covered through most of the film." This adds a new dimension to the character of The Joker.
Joker's Biggest Secret Is That He's Perfectly Sane - IMDb. The DC Universe is full of absurd criminals, but none of them is as unhinged as the Joker. His insanity has, time and time again, helped him escape death row; if he isn't in his right mind, he isn't fit to stand trial for his crimes.
How did Joker torture Jason Todd? - Quora. Joker faked Jason's death & sent it to Batman, ensuring that Batman would never try and find Jason. Then, he kept him in Arkham Asylum and tortured him for almost 2 years.
TLDR: Superman didn't save Jason because he was being tortured by Lex Luthor at the time in order for Luthor to create Conner Kent/Superboy. This is why he wants nothing to do with Superboy once he appears.
By 13, Jason was running around as Robin II. When he died, it said on his death certificate that he was 15 (and still undersized from his time living on the street).
Batman has apologized and attempted to help Jason move past his trauma several times; even as recently as last year's 3 jokers miniseries, but Jason wouldn't meet him halfway.
Jason chose to take over the moniker so he could own what the Joker did to him and use it to become the Joker's destruction. This set the Red Hood on a path to become a brooding, bitter anti-hero who often crosses lines that others in the Bat-family won't.
Jason Peter Todd is an anti-villainous vigilante originating from DC Comics. He is the second Robin after Dick Grayson. During the events of A Death in the Family, Jason was apparently killed by the Joker. He would later be resurrected as the Red Hood, taking his killer's former mantle.
when he was kidnapped by the Joker, Drake was implanted with a microchip that encoded the Joker's DNA with nanotechnology, into him. Over time, the Joker resurfaced and periodically assumed control of Drake's body.
Joker beats the boy brutally with a crowbar and then leaves him and Sheila in the warehouse with a time bomb. Sheila and Jason try desperately to get out of the warehouse but are still inside as the bomb goes off. Batman arrives too late to save them and finds Jason's lifeless body in the rubble.
The Joker shoots and paralyzes Barbara Gordon and kidnaps her father, Commissioner James Gordon. He takes Gordon to a run-down amusement park, where he cages him in the park's freak show. He forces Gordon to view blown-up photos of a wounded Barbara, lying nude on the floor after the shooting.
Enraged, he goes to Ra's al Ghul's mansion and demands the truth about Jason. Ra's reveals that he switched Jason's body and revived him in the Lazarus Pit because, as the one who hired the Joker as a distraction from his own activities at the time, he felt responsible for the boy's death.
Jarro grew attached to Batman and even often calls him “father”. He wanted to prove to Batman that he can be the best Robin and even convinced Batman to give him a chance. Jarro became the new Robin and was even said to be Batman's favorite Robin, admitted by Batman himself.
Believing Batman's methods for delivering justice were too soft and ineffective, Jason decided to take up the mantle of the Red Hood so he could punish evildoers with his own brutal sense of justice. The Red Hood was originally a disguise worn by the Joker before he was transformed into a laughing maniac.