"The wrath of God is being revealed from heaven against all the godlessness and wickedness of men." Romans 1:18
In the inspired letters of Paul, we read of God's wrath being "stored up" for the day of judgment (Romans 2:5) and that God's wrath is coming because of sin (Colossians 3:6). And the whole tenor of Revelation warns us of the wrath to come.
Having then established the grim reality of God's wrath, how are we to understand it? God's wrath arises from his intense, settled hatred of all sin and is the tangible expression of his inflexible determination to punish it. We might say God's wrath is his justice in action, rendering to everyone his just due, which, because of our sin, is always judgment.
Why is God so angry because of our sin? Because our sin, regardless of how small or insignificant it may seem to us, is essentially an assault on his infinite majesty and sovereign authority. As nineteenth-century theologian George Smeaton wrote, God is angry at sin "because it is a violation of his authority, and a wrong to his inviolable majesty."
Here we begin to realize the seriousness of sin. All sin is rebellion against God's authority, a despising of his law, and a defiance of his commands."
- Jerry Bridges, Holiness Day By Day