Fate doesn't cause damage to the player—it sounds like someone probably just got attacked during the animation. The Sword of Fate in fact does increasing amounts of healing to the party each time you use it, to a maximum of your current rank * 10.
Rank disparities do increasing amounts of damage based on the gap. A Rank III ability attacking a Rank II enemy will do 1.5x damage, but a Rank III ability will do 2x damage.