Why can't someone earn his way into heaven? Because man is a sinner. The Bible says, “For all have sinned, and come short of the glory of God” (Romans 3:23). Sin is transgressing God's law and includes such things as lying, lust, cheating, deceit, evil thoughts, and immoral behavior. Just think: if I were to sin just 3 times a day, in one year I'd have over 1000 sins. If I lived to be 72, I'd have over 72,000 sins. Imagine walking into a court trial with 72,000 speeding tickets. The judge would quickly lock me up.
Because man is a sinner, he cannot save himself. If you wanted to save yourself by good deeds, do you know how good you would have to be? The Bible says, “Be ye therefore perfect, even as your Father which is in heaven is perfect” (Matthew 5:48). That's a tough standard. Even if we're 99.9% good and only 0.1% bad, God still cannot let us into His heaven.
Think of it in terms of an omelet. Let's say you were having company over and decided to make an omelet. You used 6 good eggs, but the 7th was rotten. You couldn't serve that omelet to your guests even though most of it is good, and just like that omelet, we can't serve our life up to God. Do you see why it is impossible for anyone to earn his way into heaven by being a mostly good person?