Paradoxes from Jesus: Prince of Peace

A bearded smiling man in long dazzling white robes carrying a peaceful lamb is the iconic image of Jesus of Nazareth. We know him as the "Prince of Peace". Even agnostics and followers of other religions and philosophies admire him as a great prophet or good teacher. What did he teach? I think most would (and do) say that he taught "all people to love and be at peace with their neighbors." Jesus" and peace seem to be parallel ideas. What do we find though when we read about Jesus... 
Zechariah prophesy over Jesus when he was a child that he would, 

"... give light to those who sit in darkness and in the shadow of death, and to guide our feet into the way of peace." Luke 1:79

Jesus instructs his disciples to bless the households of those who take them in while proclaim the gospel. 

"Whatever house you enter, first say, 'Peace be to this house!'  And if a son of peace is there, your peace will rest upon him. But if not, it will return to you." Luke 10:5-6

In the famous Sermon on the Mount Jesus says, 

"Blessed are the peacemakers, for they shall be called sons of God." Luke 5:9

It seems however that people contemporary to Jesus' ministry thought the very same things that we modern readers think because Jesus had to dispel these misconceptions.

"Do not think that I have come to bring peace to the earth. I have not come to bring peace but a sword. For I have come to set a man against his father, and a daughter against her mother, and a daughter-in-law against her mother-in-law. And a person's enemies will be those of his own household." Matthew 10:34-36

See Luke 12:51 for the same quote. 


What is the sword that Jesus brings? What is the peace that Jesus proclaimed?