Why does God put up with sin?

Simply put, He endures with great patience those who are under His wrath in order to show mercy to some (Romans 9:22-25). He patiently endures sin to show maximum mercy to those He chose in Christ from before the foundation of the world. It brings Christ greatest glory for the greatest number of people to be praising the glory of His grace (Ephesians 1:3-6). All things were made by Him, through Him, for Him, after Him, and in Him all things hold together. He, through the cross, purposes to reconcile all things to Himself (Colossians 1:15-20).