olive branch

I'm wondering why the olive branch means "offer to make peace". So I got the explanation from http://www.y920.com

The origin of using the olive branch as a symbol of peace lies in ancient Greek culture. In ancient Rome too, those vanquished during war used to hold an olive branch to indicate that they were pleading for peace. According to Christian mythology, during the great Flood, a dove sent in search of land by Noah, returned with an olive branch. This was seen as a sign that God’s fury against mankind had abated, the floodwater was receding, and land was in sight. According to some, an olive branch signifies peace as olive trees, because of their slow growth, are not cultivated during times of war and, therefore, considered peace-time trees.