“Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.”  
2Corinthians 5:17

The Bible tells us:
“Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:”  Romans 5:12
Every man that was born by the first man- Adam, every man that could trace his lineage to Adam, was born in sin and born a sinner, he says death passed upon all men, for that reason- all have sinned!
No man is called a sinner because he did something bad, he is called a sinner because he came from the lineage of sin, so every person that could trace his lineage back to Adam in one form or another was a sinner and was subject to death. This is why, just doing nice things or being moral will not make the unbeliever right with God, his sin is not because of what he did but because of who he is!
If his being a sinner is not because of what he did but who he is(because of what one man did), then his being righteous would not be because of what he does, but who he will be (because of what another man has done):
“For as by one man’s disobedience many were made sinners, so by the obedience of one shall many be made righteous.”  Romans 5:19
Jesus brought salvation to the world and when you believe in him, you are not just saved from perishing, you receive something- a life, meaning the old you with the old life have died, and then you receive the new life he brought and become a new creature! He doesn’t just tell you what to do, he changes who you are! Because you are new, you are cut out from the lineage of Adam and sin, because you are new- you are now righteous and can live that righteous life.
“For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.”  2Corinthians 5:21