That is not saying that Jesus died in humanity's place as a substitute! God bless you. The fact is that God is not saving the old man! God bless you.The Bible does teach penal substitution, however there is so much more to it. Back in the early church they didn't have theories. They didn't give labels to things like we do now. Most (all?) of what we have as theories today, cover various aspects of Christ's death on the cross, to include penal substitution. Christus Victor, Ransom Theory, etc.
Paul tells us in Galations that God took our writ of offenses and nailed them to His cross. As early church father's said (a number of them), Jesus paid a penalty we could never hope to pay.