I know you probably hear this every day, but I'm your biggest fan

from Eminem (Ft. Dido) – Stan Lyrics on Rap Genius

Meaning

This is a cliche line used by fans to show their passion for the person that they admire

Paradoxical : if he is conscious that lots of people say this same thing to Em, who “hear(s) this everyday”, why should Stan be the one who is truly Em’s “biggest fan”?
This line highlights one of Stan’s biggest problems, i.e. that even though he can imagine that thousands of other fans send letters to Em just like him, he peremptorily, arbitrarily considers himself as the “biggest” one, thus his letters as the most important ones and the first ones Em should answer to; that’s why he allows himself to think of his relation with Em as direct, special and even intimate. But facts won’t meet his imagination.

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