Yes. I'm a Christian, so I believe there is only one answer. You're not a Christian though. So, I'm going to explain the problem, or why we have to be reconciled with God.
We don't follow God. We follow our own path. It may be intentional defiance or it may be lack of faith in God. The thing is, God is the creator and ruler of everything. He has the right to everything. He isn't a terrible ruler trying to harm his subjects or torture them. When we turn from him, it's about the equivalent of the servants of a good king or ruler refusing to do what he says and what the law demands and completely refusing to serve him, regardless of intent. This type of crime is treason. Even if you forget about all of the other bad things a person does, this crime alone is enough to earn death. God's punishment is not only the death of our bodies (separating our souls and spirits from our body) but the death of our spirits (separating our souls and spirits from him). This is basically what we ask for when we follow our own path apart from him, but it really sucks. I posted a little bit about hell a few posts back. Eternally separated from God, without hope.
So, that's why we need to be reconciled. We take off on our own path. We run away from God. We are apart from him, and need to come back to him, but our sins, our treason, separates us. We owe him a debt, a debt that must be paid. This is why works don't get you into heaven. You can't work your way to heaven. The good things you do don't erase the bad. I described us as running away from God. This is like the parable of the son that demanded his inheritance from his father, left with it, and spent it all. Living a good life and being careful with your money doesn't do you any good if you don't have any money and you took all the money from your father anyways, just like living good won't help you. You may do less bad things, you may sin less, but you never really stop sinning and you still haven't done a thing about your previous sins. All you might do is slow your present rate of sin. Those sins will get you into hell.
That is why I think good works don't cut it with God. You don't even really stop sinning, so it really doesn't matter. You can work and work and work, but you can't undo what you've done. You can try to lessen the effects, but you can't erase what you did from history. Not spending money when you owe debt is a good idea, but unless you can pay back the debt, it doesn't do you much good. You've got to pay back the debt, but you can't. Works don't pay back anything. So, any idea of getting to heaven by works is out.
You may be wondering why God doesn't just say oh well, they all screwed up, I'll let them slide. After all, he's supposed to be all loving. The thing is, he's also just. So, even though he loves you and he really doesn't like to do it, he will send people to hell. A truly just judge demands the penalty be paid and that the law be upheld. Someone has to pay the penalty. Not that God is out for blood, but the debt must be paid. You must pay for something like a speeding ticket in human courts; in God's court, you must pay for treason, and the price is your life.
So, we have to pay with our life. We can't pay with another person's life because they have to pay themselves can't really offer anything. They owe debt too. They are going to have to pay with their life. They can't give you more life because they don't have extra life to give. Now, if we had extra life, if our sinful selves could be put to death and somehow we could still live, we would be fine.
The Jews used sacrifices to pay. The thing is, animal sacrifices don't mean too much. You killed a perfect lamb. It was spotless. It never did anything that bad. It was a lamb. A lamb can't exactly give you new life so that when your sinful self dies, you don't. There isn't really anything special about a lamb, except that it was symbolic (which is why people in the old testament don't all go to hell. They put their trust in Jesus, but since he wasn't exactly around on Earth at the time, they demonstrated their trust by sacrificing lambs and other animals, which was symbolic of Jesus's death).
I think I've covered the way most religions try to pay for the debt. I think that most religions go along the lines of "work your way into happiness." Even the Jews had to sacrifice animals (and with all the associated rituals, it was work). Doing good deeds is fine. I am not in any way saying that you shouldn't do good deeds, but they aren't enough. Most of the other religions will scream at you to work harder to gain paradise. You can never work hard enough. You can't work so hard that it's like all of the screw ups you made in life are erased like they never existed. The other religions want you to do good things, but they can't help you do them. They can't help you be reconciled to God. They can just tell you what to do. I could spit out a bunch of things for you not to do, but that doesn't really help you. There is a quote from a famous Christian author John Bunyan stating "the law commands but gives me neither feet nor hands" and that basically sums up all of the work religions. You can tell someone to work hard, but you can't make them. You can tell someone to avoid all sorts of sins, but you can't make them do anything. In the quote, he was referring to the old testament law (I think) but it applies to every law. There is no power in the law. Principles may be fine, rules may be good, but they have no power to save you. You need life, not rules. If you just try to live by rules, you will fail. They can't hold you to them. They give you no power to be perfect. They can't cancel out your sins. They just serve to show you that you fail. That's one good thing about laws. When you screw them up plenty, you realize that you can't do it. You can't be perfect. You will sin. Laws expose sin and wrong doing (which some people may need). They do not correct them or pay for them, which is what we all need.
Right now, we have a fairly gloomy picture. We can't work our way into heaven, because we will fail anyways, and our works don't erase our sins. The penalty for sin is death. Not pleasant. We need new life. We can't exactly borrow our neighbors, because they need new life too. But, God does love us. So, he sends the solution. Jesus.
Jesus, fully God, but also fully human. God in flesh. Called the son of God because he was conceived in Mary by the power of God. Being fully God, he had the power to resist temptation. He could live with God because he was God. He didn't run away from God. He lived perfect. Being God, he had life. He also had no debt to pay. We, on the other hand, need life, life that doesn't have any debt to pay. We need him. He really doesn't need us, but he loves us. So, he takes our punishment. He takes our debt. He takes being cut off from God. He takes what we should have to pay. He does a bit more. He takes our sins and puts them on himself. He takes those sins to the grave. He then raises from the dead. He is God. Death does not have power over him.
He takes our sins, and we gain his righteousness. He takes our death, and we take his life. It's like our sins and our sinful self is crucified and dies, and our new self, the one full of Jesus, lives. Not that Christians are perfect. We have our new life, but the old one doesn't completely go until the end. Our sin is paid for, though. So, any punishment that should be ours is Jesus's. It's like he steps up, takes our sin on himself and brings it to the grave, then gives us life (I know I've already said this). We are no longer condemned by God, because all our sin is on Jesus. We are free from our debt.
So, do we go on sinning and living our life like we did before? The answer is no. Okay, we still sin, but our lives are different. Why? Because Christ lives in us. He lives through us. So, we still sin, because we are still prone to sin, but we do not find pleasure in sin because we have Jesus living in us, and he does not like sin. So, we try to do what is right. We still screw up. But, we don't use Christ's payment as a free pass to do whatever we want and sin however we like because we don't like to sin. His nature lives in us. It is what survives in the end. Our old bodies will die. Our souls will not, and we will get new bodies. Our old self will be completely gone.
So, we looked at our debt. We looked at why works don't reconcile us to God. We look at how, when Jesus took our sins, we are reconciled with God because Jesus carried them away and paid away our debt, so God accepts us like he wanted to. I probably didn't do the best of jobs at the end, so if you have any questions, please ask. If you think there is another way we could be reconciled that I didn't cover, please tell me.
The full quote from the Christian author and my ending note:
"Run, John, run the law commands,
But gives me neither feet nor hands;
Far better news the gospel brings:
It bids me fly; it gives me wings."