Peace doesn't come naturally to us. It did in the garden, but when Adam and Eve decided to ignore the words of God, they set the pattern - and the destination - for all of us. Since then, the moments of peace have been rare.
Jesus came to bring a peace which is impossible without him. It's impossible because it's a standard we are incapable of attaining on our own, based upon having a peaceful relationship with the One who created us. If we are at war with Him, we will never experience peace.
The Psalmist wrote, "The Lord gives strength to his people; the Lord blesses his people with peace" (Psalm 29:11). It makes me realize that peace, in fact, requires strength, and that strength come from the Lord himself.