In this chapter, Keller doesn't defend the existence of God as much as he defends the Penal Substitutionary Theory of Atonement. He gives 2 primary reasons it is necessary. First, he maintains that forgiveness entails "absorbing the debt of sin yourself." The cross was God's way of absorbing the debt of sin. However, we all have forgiven someone and "absorbed the debt" rather than seek vengence or demand reparation. This doesn't entail us nailing ourselves to a cross. We experience the pain of betrayal, the wounding by hurtful words, the loss of property by theft and choose not to lash out. This is absorbing the debt, something God did just by experiencing the pain of our betrayal, sin, and disbelief. I don't exact revenge on my oldest son when he rolls his eyes, refuses to answer me, and makes rude comments(though I may be very tempted to yell and scream). I tend to absorb the pain and forgive. I may punish with time out as a deterrant to future rude behavior, but it doesn't satisfy my desire for retribution.
Secondly, Keller supports the need for the death of Jesus by maintaining that God would not be a God of love if he wasn't willing to "become personally involved in suffering, the same violence, oppression, grief, weakness, and pain that we experience." I would maintain that by being in relationship with humanity, God experiences suffering. Jesus also experienced many of these things while on earth, even before his death. Also, it is never reported in scripture that he experienced every type of trauma that has befallen human beings. So, I don't know how we could argue that death was somehow a required experience.
I do know there are many scriptures that would support the Penal Substitutionary Theory of Atonement. However, there are other scriptures that offer other views.
There are many issues I would like to address regarding Penal Substitution, but I don't have time at the moment. Maybe I will turn that into a mini series.