The peace the angels were singing about was not a peace between men; they were rejoicing that there would be peace between God and man. When Jesus prophesied division and war in Matthew 10, he was speaking of relationships between men.
Through the Old Testament law, God began to release His wrath on man's sin (Romans 4:15). It wasn't the wrath of Satan that Jesus suffered on the cross.
He suffered the wrath of His Father (Isaiah 53:10-12; 2 Corinthians 5:21). The Father placed His punishment for our sins on Jesus. This ended the war between God and man. This is the peace that the angels were proclaiming.
As a result of men receiving this peace from God there have also been many cases of reconciliation between men, but that is an effect; not the actual peace that was spoken of.
Through Jesus, we now have peace with God (Romans 5:1). God is not mad at us. He isn't even upset. We have been accepted through Jesus (Ephesians 1:6).
Believe the good news that through Jesus, the war between God and us is over.