Biblical salvation is so narrow and only through Jesus because it cannot be any other way.  Let me explain, step by step.

1. God is perfect, and he reveals what is right and wrong from his character (Matthew 12:34; 1 Peter 1:16; Titus 1:2).  So, morality is based on the nature of God, not arbitrary decisions of God or of man.
2. God tells us to be holy because He is holy (1 Peter 1:16).  Therefore, the standard of perfection is God, not imperfect people.
3. God gave us the Law, and when someone breaks that Law there is of necessity a punishment (Exodus 20:1-17); otherwise, a law is not a law.  It would be a slogan.
4. God, as the Law Giver, has the right to execute judgment upon anyone who breaks his Law.  Therefore, he needs to be satisfied according to the law.
5. We have all sinned (Romans 3:23), and everything we do is affected by sin (Jeremiah 17:9).
6. Since all we do is touched by sin and is impure, and since God requires perfection (Matthew 5:48) as well as holiness (1 Peter 1:16), then His standard is unattainable by us because we are not able to do anything good enough to merit favor with God (Romans 3:10-12; Jeremiah 17:9; Galatians 2:21).
7. Since we are incapable of making ourselves right with God, the only one left to make us right with Him is Himself.
8. Jesus is God in flesh (John 1:1, 14; Colossians 2:9; Philippians 2:5-8; Hebrews 1:8) who was born under the Law (Galatians 4:4) and who never sinned (1 Peter 2:22).  Therefore, he is perfect and holy.
9. Jesus bore our sins in his body on the cross (1 Peter 2:24), died with them, and rose from the dead (1 Corinthians 15:1-4).  In doing this he satisfied the requirements of the Law which is death (Romans 6:23).
10. We must trust in the work of Christ, and not our own, because that is all we can do.

So, since the only way for us to be forgiven is by the work of God, and Jesus is God in flesh, then the only way to be saved is through the single person of Jesus.  That is why Jesus said in John 14:6, “I am the way, and the truth, and the life; no one comes to the Father but through Me.”  Also, It says in Acts 4:12, “And there is salvation in no one else; for there is no other name under heaven that has been given among men by which we must be saved.”  There is no other way to be saved because “…if righteousness comes through the Law, then Christ died needlessly,” (Galatians 2:21).  And, “…if a law had been given which was able to impart life, then righteousness would indeed have been based on law,” (Galatians 3:21).