Robin, hon, can you explain to me why there is bad blood between Bruce and Jason?

I could go on and on and on but in the name of both our sanities I will summarize.

Bruce found orphaned street kid Jason stealing tires from the Batmobile, adopted him and made him Robin (which pissed off original Robin, Dick, bc it wasn't Bruce's mantle to give away but I digress). Things are good for a while. But Jason had a lot of unresolved anger and depression from year living on the streets, he became reckless in the field and was overly aggressive with criminals (esp those who abused women or children like same boy). Bruce, angry and worried, pulled him from heroing to get him help. Only Jason didn't listen and when he heard his birth mother was in trouble, he ran across the world to go help her only to be caught by the Joker. He is beaten half to death by the clown and left to die in an exploding building. Robin II and Bruce's son is dead.

It's a tragedy, Bruce mourned Jason so hard almost falling apart as Batman and Wayne. Tim Drake, avid Batman fanboy who uncovered their IDs through investigatory work, tries to bring Batman and Nightwing back together to help stabilize Batman. Once the dust settles, Tim is chosen to be the new Robin, Dick and Bruce have started to reconcile and real healing is beginning to happen. All is well right?

Wrong! Turns out Jason has been brought back to life (pick your version, Superboy Prime punching reality from the inbetween space he's trapped in or Ra's al Ghul stealing the body and Lazarus Pitting him). Jason comes back mundo scrambled and it takes him awhile to get his bearings under him. All he knows is when he looks around, Batman has replaced him with another Robin and appears happy as can be. Underlying anger issues + genuine hurt feelings + post resurrection mind fuck means Jason is Pissed. He dedicates himself to learning the deadly arts Batman never taught him.

He returns in the Under the Red Hood comic (chef's kiss) as the criminal vigilante, Red Hood, who uses terror and murder to become Gotham's premiere crime lord. He lets Bruce and everyone know who he is, as dramatically as possible, with heart breaking results.

This ended up being a very long explanation to say: Jason had some tension with B before he died, blamed Batman for letting him die and then quickly replaced him not long after. He believed B didn't love him and saw his Robins as expendable pawns used to uphold his moral high ground version of justice that didn't fix Gotham. It's why Jay went on his murder spree to "do what Batman couldn't and save Gotham". He's especially mad Bruce didn't kill Joker, the man who murdered him.

Ofc Jay doesn't know everything, doesn't know how deeply and painfully Bruce mourned Jason, even years later. Didn't know that he did his best to prevent another Robin from happening and Tim basically forced his hand. Couldn't understand how close B came to killing Joker, not just for Jason but for paralyzing Barbara and torturing Jim Gordon. Jay brings up good points but in his post-Lazarus Pit single minded focus rage, all he could see was that his father didn't avenge him and took it personally.

From Bruce's end, his spunky, smart, big hearted child died and what came back was wrong. Red Hood Jason was hard and cruel and spat on Batman's number one rule to not kill. Bruce's greatest grief is shoved back in his face and B, who has never handled negative emotions well, doesn't do much to explain himself to Jason. In the end, he puts Gotham first by trying to stop Jason's murder spree not knowing he's reinforcing Jason's ideas on not being loved. Jason also attacks Tim which Bruce takes very personally bc he will NOT lose another Robin. Not even to his own child.

Once Jason calms down a bit and has some conversations with B, they come to an uneasy impasse where he's a part of the fam always but he's not quite ready to let go of the past and be a Bat or Bruce's son again.