This is how Black Phantom explains his plan goes in Princess Twilight Sparkle Part 1.
[Black Phantom polishes his armor]
Black Phantom: Ah, music to my ears. Now to finish what I came here for.
Princess Celestial: Hold on, just what do you think you're doing?
Princess Luna: You must reveal your plan.
Black Phantom: Oh, stripping the Tree of its magic so I can use it for my own purposes. Since destroying your precious tree, there will be no more Elements of Harmony to defeat evil, such as myself.
Princess Celestial: Ha. Your plan won't work. The tree's magic will recognize your villainy.
Princess Luna: I agree with my sister.
Black Phantom: I've already got a solution for that.
[Black Phantom clicks his fingers and Arachnix appears]