User blog comment:Skeith9/Heroic Spirits Speculation/@comment-5739199-20140518001709/@comment-5739199-20140518030216

Arc is the "reincarnation" of Crimson Moon and has the potential to become an Aristotle, and even so she became a Servant in Extra.

Remember that Tsukihime didn't take place in Extra because of the Moon Cell, so it's all fanservice