Apparently there's a bug that prevents players from creating a Hardcore Mode character. There was no character wipe in this beta patch, which seems to cause problems. Hardcore Mode (beta only) is unlocked at level 10, but having existing characters beyond level 10 prevents the game from creating a hardcore character.
Diablo III Beta Patch 14: Known Hardcore Mode Bug
Diablo III Beta Patch 14: Known Hardcore Mode…
Diablo III Beta Patch 14: Known Hardcore Mode Bug
Apparently there's a bug that prevents players from creating a Hardcore Mode character. There was no character wipe in this beta patch, which seems to cause problems. Hardcore Mode (beta only) is unlocked at level 10, but having existing characters beyond level 10 prevents the game from creating a hardcore character.