Think not that I am come to send peace on earth: I came not to send peace, but a sword.
Note 4 at Mt 10:34: This statement seems like a contradiction to some prophecies concerning Jesus (Ps 72:7, 85:10; Isa 9:6-7; and Lu 2:14), some of His own statements concerning peace (Joh 14:27 and 16:33), and what was written of Him in the New Testament epistles (Ro 5:1, 14:17-19; Eph 2:14-17, 4:3; Php 4:7; Col 3:15; and Heb 12:14). However, the peace that Jesus purchased was peace between God and man. We have peace with God (Ro 5:1). We are exhorted to take this peace and extend it to all people (Ro 12:18 and Heb 12:14), but it is also made very clear that not all people will receive it (Joh 16:33 and 2Ti 3:12). Therefore, as Jesus was explaining here, 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 who causes it, but it will inevitably come. Jesus was simply preparing His disciples. As much as we would like to see everyone receive the good news, we must not think it's strange when even our loved ones don't receive it. Jesus was rejected by His own (Joh 1:11), and we will be also (Mt 10:24-25). We must remain faithful to keep preaching the Gospel, for there are others who will receive.