Stepping into the cage with the tributes was a way for Coriolanus to show the tributes he’s like them and he empathizes, but in reality, the kids don’t see Coriolanus as someone who
can empathize with them. He’s a Capitol kid, with way more privilege than these kids have ever had. And winding up in the zoo with the tributes shows Coriolanus in no uncertain terms how the Capitol thinks of the tributes. To the Capitol, tributes are animals to be gawked at, not people to care for.