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Self love [artist unknown]
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If you're asking why a Satanist would want you to believe any particular thing, I think a significant majority of Satanists would agree: nobody wants you to believe anything in particular. Proselytism is something Satanists probably tend to hate about other religions.
But if you're wondering why Satanists believe it (or at least why the Satanists who believe it believe it -- though I expect that's a very popular belief among Satanists)...
It's kindof the whole deal with the left-hand path. The way left-hand path sort of folks will describe it to you, the right-hand path is about trying to get "closer to god" by being more "holy" to get more in god's good graces. The left-hand path is about becoming (a) god (or perhaps to recover from the right-hand-path-originated delusion that you're not a god already). To claim/own power oneself rather than to supplicate to another being. (Mind you, there are left-hand path practices centered around working with entities, but even those have as their goal to request the assistance of said entities in order to be(come) a god oneself.)
Honestly, if there's one belief more widespread among folks who identify with the "left-hand path" label than that they either are or ought to become a god, I'm not sure what it would be.
Oh, one more thing I'll say. It's probable, at least in my estimation, that a certain fairly sizeable percentage of Satanists out there may "believe" the statement "I am a god" more as an affirmation, goal, self-fulfilling prophesy, or some such than as a tenet.