Why God can't just forgive sin
Then he steals from the owner again. He feels terrible so he apologises again. Because the owner is a forgiving person he forgives him again.
Then he steals from the owner again. He apologises again, and is forgiven again.
Then he steals from the owner yet again. He feels absolutely terrible, and so he apologises and is forgiven yet again.
That's a bad situation to have happen. Even so, the principles in this situation apply to all Christians, and for people of any other religion who have an analogous point-of-view.
Well, let's say I sin against another person. I recognise my guilt and apologise to God. God forgives me.
Then I sin again, doing the same sort of sin, against another person. So I apologise to God. God forgives me unconditionally.
Then I sin again, making the same sort of mistake, some time later. I realise this and so I apologise to God. God forgives me yet again.
Is there any Christian for whom this sort of situation is not the case?
I suppose it's possible that some Christians can perfectly repent of some sins, but there are a lot of sins that will still remain to one degree or another in a Christian's life (even if most of the time they're only expressed in the head, or in a possible situation that hasn't happened).
So imagine that the thief keeps stealing again and again, and the owner keeps forgiving him. That's awfully nice of him, but does that deal with the REAL issue here? The real issue is that he keeps stealing. It's not a matter of forgiveness, in that hypothetical situation, it's a matter of the fact that he keeps stealing and needs to stop it. Forgiveness deals with the owner not taking revenge, but it doesn't deal with the fact that someone who steals all the time is a thief and needs to stop stealing.
According to the same principle, in this life Christians will never stop sinning against God and other people, even though God always forgives us. God will always forgive us every time that we honestly ask for forgiveness. But does that deal with the REAL issue here? The real issue is that we don't meet God's standards despite God's forgiveness. Because I'll bet that after we ask forgiveness we don't suddenly become sinless. God's forgiveness deals with God taking revenge, but it doesn't deal with the fact that our actions are not up to God's standards.
This is why God's forgiveness outside of Christ is not good enough to save people. What condemns people is the fact that they don't meet God's standards, and thus can't be with God forever. It's not an issue of God taking revenge, it's an issue of the fact that someone who does the wrong thing can't be with God. God's forgiveness means God won't take revenge, but if we continually want to sin, then we're not up to God's standards and can't be with God.
So God can't deal with sin just by forgiving it.
God needed a form of forgiveness that changes the heart of the person asking for it, so that they never sin again in any possible situation (which is what it means to meet God's standards).
But what kind of forgiveness can do that? Certainly nothing that the owner can give to the constant thief he forgives.
The atonement solved this problem, creating an extremely 'powerful' kind of forgiveness. Imagine all of our evil collected together in a pool of black sludge. You could say that in the atonement God poured out all of our evil onto Christ (although Christ never endorsed it) and we received Christ's perfect goodness in return. God 'gave' our evil desires/intentions to Christ in the areas where we sin, and Christ lives in us, acting perfectly, in return (Rom 6:6; Gal 2:20). So Christ in Christians will one day enable Christians to be perfect by doing everything for us in the areas where we currently sin. Christians aren't perfect only because God is waiting until the 'Day of Redemption' to apply this fully to Christians (Eph 4:30). See here for a longer account of how Christ's death takes away evil.
This is a reason why I think Christianity makes more sense than a religion where the solution to humanity's wrongdoing is for God just to forgive sin. Just like a person forgiving a thief who keeps stealing doesn't solve the thief's problems, so God forgiving our sin if we want to keep sinning doesn't solve humanity's problems.
[Edit] Clarification after someone said to me they didn't get it.
Basically, I was saying that forgiveness doesn't do a lot of things. If I forgive someone for stealing from me, then it means I won't report them or plot against them, but it won't necessarily mean they'll stop stealing. So forgiveness won't necessarily make the forgiven person better.
So the cross is a type of forgiveness where forgiveness DOES make someone better. God puts our evil onto Christ, and then the punishment for it is put on to him, and so it is no longer us living but Christ living in us, in return (Gal 2:20). Luther called it the 'great exchange'.
Philippians 3:8b-9a: "for whose sake I have lost all things. I consider them rubbish, that I may gain Christ and be found in him, not having a righteousness of my own that comes from the law, but that which is through faith in Christ"
And 2 Co 5:21 is good also.