Jason Todd: Robin, Red Hood, Arkham Knight Appreciation 2021

[Zaresh]

Dragging the kid around and leaving him in an alley, hoping nothing happens to him while he goes into a druglord's den is the further thing away from protecting him. And he's at the very least in friendly terms with Barbara, so why not get her to set a safe place for the kid to stay with? In the past the safety of others has always been Jason's top priority, not killing criminals.

Because that's the sort of thing all heroes (all of them) often do and we are expected to now think about.
Because stopping to ask Barbara and leave the kid with the cops or something wouldn't make for a story and is narratively boring and kills the pathos created by the meeting with the kid and the dossed mom.
Because Jason was emotionally very stressed.
Because he meant to be there to find a regular working place, not a drug factory, if I recall.
Because he entered the building thinking he would find the parent and exit with him alive and reuniting parent and son, who would be finally safe.