Why was it necessary for Jesus to be crucified to save us from our sins.

This questions centers on the central theme of the entire bible, mankind's reconciliation to his original relationship with God. 

The first man, Adam, sinned by disobeying God's instruction not to eat from the tree of knowledge of good and evil  (Genesis 2:17). As a result, he was banished from the Garden of Eden and fell from the perfect state in which he was created (see Genesis 3). 

In Genesis 1:27 we read that God created man in his own image. This suggests that man had qualities similar to those of his creator. Qualities such as a free moral agency; powers of reason and memory; attributes of justice, benevolence and love. Man was created perfect, both mentally and morally. By succumbing to the wiles of the adversary, man began his downward fall and his separation from God. Man was under the condemnation of death. 

We read in Psalm 51:5 that man is born in sin, resulting from Adam's violation. The entire race of mankind has come under the penalty of sin – death and separation from God. This is further verified in Romans 3:23, "For all have sinned and come short of the glory of God". 

Jehovah is a just and loving God.  His justice dictated a penalty for Adam's disobedience and his love provided the remedy. In 1 John 4:10 we read, "Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation (atoning sacrifice) for our sins". God's love and justice provided a ransom or redemption (Psalm 49:7) from Adam's original sin and its effect on his posterity (see Psalm 51:5). 

Because Adam was a perfect man when he sinned, justice requires a perfect man to pay the ransom price for his sin.  In Colossians 1:12-14 we learn that we are redeemed through Jesus' blood and that Jesus was God's son. John 3:16-17, “For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. For God sent not his Son into the world to condemn the world; but that the world through him might be saved”. 

Again, a perfect man (Adam) sinned thus a perfect man (Jesus) had to pay the penalty for sin – death! 1 Corinthians 15:22, “For as in Adam all die, even so in Christ shall all be made alive.”

Crucifixion was a common means of execution in Jesus' time. It was often used as a means of furthering the pain and anguish of the condemned and a form of humiliation. It is important to realize that Jesus' crucifixion was not forced by God, or man. John 10:18 reads, "No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again."  See also Philippians 2:7-8. 

We must not allow the method of Jesus' death to cloud our understanding of WHY Jesus was crucified.  He satisfied justice and paid the corresponding price, THE RANSOM, which leads to the eventual redemption of all mankind from sin and reconciliation to Jehovah.