"No one calls us home anymore," Sang-woo says, and he means it as a justification. An excuse. His life is empty, he is no longer a child to be cared for, no one calls for him and he has no home to go back to.
Gi-hun could have offered the obvious answer. He could have pointed out that Sang-woo's mother still calls him, that she talks to Gi-hun about her son whenever she sees him. We as the audience know that she asks if Gi-hun has heard from him, later, when she can't reach her son and worries if he's okay.
Gi-hun could have heard the excuse, the plea to give up, and he could have argued with Sang-woo or let him give up.
Instead, Gi-hun sees a reason for hope. He sees an opportunity. He hears, "No one calls us home anymore," and he holds his hand out immediately and says, "Let's go home."
Even if no one else will call Sang-woo home, Gi-hun will.
But Sang-woo doesn't take his hand. Sang-woo grabs the knife and takes his own life, instead, because the truth isn't really that no one calls him home anymore.
The truth is that Sang-woo is the one who stopped listening when they called.
