The Gospel
If you were standing in front of God and He asked you "Why should I let you into Heaven?", what would your answer be? If your answer involves anything about you being a good person or doing good works, I pray that you take what is written below to heart, because it is the biblical truth.
If you believe you are a good person, there is a good chance you believe that because you are comparing yourself to other humans. However, the Bible tells us that "there is no one who does good, not even one" (Romans 3:12) and that we "all have sinned and fall short of the glory of God" (Romans 3:23). This means that we are judged according to God's perfect righteousness, and hence, even one singular sin will separate us from God's righteousness.
Just to mention a few sins, have you ever stolen (the Eighth Commandment), lied (the Ninth Commandment), or used the Lord's name in vain (the Third Commandment)? How about committed adultery (the Seventh Commandment)? You may be thinking you haven't violated this Commandment, but Jesus says "But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart" (Matthew 5:28). Therefore, if you have ever lusted, you are guilty of committing adultery.
If you answered these questions truthfully, you probably have multiple, if not all, of these titles applicable to you - a thief, liar, blasphemer, and adulterer (and we've only looked at four of the Ten Commandments)! If you think "but I've only done that once and I won't do it again", that won't allow you to escape God's judgement, because He is perfectly just and holy. For example, if someone is on trial for stealing a car and they say "It was only once, I promise I won't do it again", will a good judge let that person free? No, they will get put in jail as punishment for what they did. Similarly, because God is perfectly just, He must punish us for our sins, since wickedness can not stand in the presence of holiness.
Now, if God were to judge you according to His laws, would you be innocent or guilty? And hence, would you go to Heaven or Hell? I hope at this point you see that you are guilty and would go to Hell; however, there is great news for us sinners. ↓↓
The Good News, or the Gospel, is that God provided a way for us to reach eternal life through His only Son, Jesus (John 3:16). Jesus, who is both fully God and fully man, lived a sinless life – something we were unable to do – and bore the wrath of God on the cross in our place. Three days later, Jesus resurrected just like He said He would, conquering death. If we repent of our sins and put our faith in Jesus Christ as our Savior, since we can not save ourselves, we will receive everlasting life! As believers, Jesus' righteousness is imputed to us and we are viewed as righteous in front of God. How grateful we should be that out of grace, our Savior has saved us and provided us with redemption (Ephesians 1:7) and new life (2 Corinthians 5:17).
Returning to the initial question of "why should you be allowed in Heaven?", the answer is simple: I do not deserve it because I am a sinful human, but I believe that Jesus suffered on my behalf on the cross and was raised three days later. Since I have repented of my sins and put my trust and faith in Jesus as my Savior, You say that I may have eternal life.