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You know the kids in the schoolyard who think they're totally invincible? The ones who say, "Punch me as hard as you can. No really – as hard as you can." They're completely confident that they won't get hurt, no matter what you dare them to do. That's exactly what Balder's like. When his mom, Frigg, makes just about everything in the world promise not to harm her son, he becomes almost impossible to kill. That's why Balder and the Aesir start playing a game where they all chuck things at him – stones, arrows, probably even Thor's hammer – because it seems like nothing can hurt him.
The biggest connection between Balder and the Greek hero Achilles is that their mothers tried and failed to make their sons immortal. In Achilles' legend (as told by Homer in The Iliad), Thetis dips her son in the immortality-bestowing river Styx, but holds him by his right ankle, leaving that part of his body vulnerable. Balder's vulnerability is also caused by his mother's omission. She failed to require mistletoe to take the oath not to harm Balder, although she required it of everything else in the world. In both stories, these seemingly small vulnerabilities are the means by which the heroes can be vanquished.