It teaches that while the world runs on cruel mathematics (Equivalent Exchange), the human heart does not. As Edward Elric says: "There's no such thing as a painless lesson—they just don't exist. Sacrifices are necessary. You can't gain anything without losing something first. Although... if you can endure that pain and walk away from it, you'll find that you now have a heart strong enough to overcome any obstacle."
Unlike many long-running shonen (like Naruto or One Piece ) where side characters fade into irrelevance, every single character in Brotherhood matters.
