OK. We all sin, every day. None of us are perfect - we lie, we hurt others (even unintentionally), we are envious, we don't do the good that we should do. None of us are able to come before God on our own efforts, because he abhors sin.
God saves those who believe because he attributes Jesus' righteousness to them. Jesus did not sin, and when he died on the cross he took the punishment for the sins of the whole world. Because God loves us and wants us to come back to him, the only thing that he requires is this belief - it's an open invitation which every single person is capable of taking up.
If you don't believe in Jesus you are not accepting God's offer, but instead are setting your own terms. I want to be saved/forgiven/go to heaven, but I want to do it my way, not your way.
A wrong action requires a consequence for that person to be restored. If someone murders another person, they go to prison. If we break something, we pay for it, or make amends. If a child hits another child, they say sorry. This is what justice is, and most of us manage to abide by society's rules quite well. But God's standards are perfection, which no one can hope to attain, hence his offer of salvation.
This is why the entire point of Christianity is not about being good. It's about how we are not good, at all. Many great Christians describe themselves as the worst of sinners, because they realise how far they fall short of the true definition of good (morally excellent, virtuous, righteous).
Lifeisgoodish you're exactly right that trying to live a good life in this life is its own reward, and brings many benefits. But a Christian's aim in life is not to be good, but to love and glorify God and try to please him, and what pleases God most is when we realise that we actually need him.