This statement of peace in Matthew 10:34 seems like a contradiction to some prophecies concerning Jesus and some of Jesus' own statements concerning peace, as well as what was written of Him in the New Testament Epistles.  The peace that Jesus purchased was peace between God and man.  We have peace with God (Romans 5:1).  We are urged to take this peace and pass it to all men, but it is also made very clear that not all men will receive it.

Peace can only come when we relate to God on the basis of faith in what He did for us, instead of what we do for Him.  A person who is thinking that he must perform up to some standard to be accepted by God will have no peace.  That puts the burden of salvation on our shoulders, and we can't bear that load.  We were not able to live holy enough to please God before we were saved, and we are not able to live holy enough to please God now that we are saved (Hebrews 11:6).  We were saved by faith, and we have to continue to walk with God by faith (Colossians 2:6).  Not understanding this has made many Christians, who love God, unable to enjoy the peace that was provided for them through faith in Jesus.

The Gospel will always produce opposition from those who don't receive it.  This "sword of division," even among family members, is not God's will, nor is it God that causes it.  But, it will inevitably come, and Jesus was simply preparing His disciples for that time.  As much as we would like everyone to receive the good news, we must not think it is strange when even our loved ones don't receive it.  Jesus was rejected by His own, and we will be also. We must remain faithful to continue preaching the Gospel, for there are others who will receive.