The Christian Perspective
Burning Korans is certainly an incendiary activity.
But seriously, I'm not in any position to say why the Dove World Outreach Center is burning Korans. You would do far better to ask them instead of us.
I can, however, tell you what they seem to say on their website.
It appears as though they believe that they can draw attention to themselves among Muslims and others considering Islam. Once they have the attention of these individuals, they seem to think that they will be able to share the truth of Christ with them and expose the lies of Islam.
It may work. Or it may not.
The Christian God has, throughout history, frequently ordered the destruction of idols and altars to false gods, so this would certainly not be totally outside the realm of acceptable Christian behavior. It would be completely inappropriate to universally call the destruction of false religious objects an unchristian thing to do. To do so would be to condemn the Christian scriptures themselves.
You are to tear down their altars and smash their sacred pillars and cut down their Asherim -- for you shall not worship any other god, for the LORD, whose name is Jealous, is a jealous God.
But thus you shall do to them: you shall tear down their altars, and smash their sacred pillars, and hew down their Asherim, and burn their graven images with fire.
Now on the same night the LORD said to him, "Take your father's bull and a second bull seven years old, and pull down the altar of Baal which belongs to your father, and cut down the Asherah that is beside it; and build an altar to the LORD your God on the top of this stronghold in an orderly manner, and take a second bull and offer a burnt offering with the wood of the Asherah which you shall cut down."
And many of those [new Christians] who practiced magic brought their books together and began burning them in the sight of everyone; and they counted up the price of them and found it fifty thousand pieces of silver.
Having said all of that, burning Korans is not something that I personally have ever engaged in. I suppose if I were on a desert island and needed to cook an animal I had just killed, and all I had for cooking fuel was a Koran, I would thankfully torch the thing. But apart from a circumstance like that, I would prefer to point out passages in the Koran that demonstrate the logical impossibility of Islam, rather than removing said passages from people's view by burning them.
The God of Islam, for example, is always just (Quran 4:40, 2:272, 2:281, 3:18, 3:108, 50:29 etc). However, He sometimes forgives people, ignoring justice (Quran 4:23, 4:25, 4:43, 5:18, 8:29, 28:16, 39:5, 57:28, etc). So He is always just and yet it is not the case that He is always just, at the same time and in the same way. The Biblical God does not have this problem, for perfect justice was wrought upon Jesus Christ, who took our punishment in our place, enabling forgiveness without denying justice (Isaiah 53:5; John 15:13; 1 John 2:2; 1 John 4:10).
It is interesting to see how much condemnation this little church has drawn upon themselves. The mainstream media, Hillary Clinton, and even General Petraeus roundly condemned them. Funny... I really don't remember this kind of condemnation falling on South Park.
Dove World Outreach Center's Ten Reasons to Burn a Koran