Jason Todd's origin was more about the grittier side of Gotham. He came from a tough background on the streets. Batman took him in as Robin to give him a better life and a purpose. But his time as Robin was cut short by the Joker's heinous act. His death then became a major turning point in Batman's life, making Batman more brooding and vengeful. His origin as Robin was like a brief but intense flash of hope that was snuffed out too soon in the dark world of Gotham.
The origin of Robin in the Batman universe is deeply intertwined with Batman's own journey. As mentioned before, Dick Grayson's origin was born out of tragedy. His parents' death led him to Batman, who saw in him not only a boy in need of a home but also someone with great physical abilities due to his trapeze training. This was the start of the Robin legacy. It was a way for Batman to have a partner, someone who could be a symbol of hope in Gotham just as he was, but also a young face to show that even kids could make a difference in the fight against crime.