Why does Shakespeare emphasize how his mistress is different from from others? Does he want to insult her?
I assume you mean by Shakespeare's "mistress" the Lady of whom he writes in the Sonnets. In particular, I am again assuming that you are referring to the Lady spoken to in Sonnet 18. This is the sonnet that begins, "Shall I compare thee to a summer's day?" This is a sonnet that is specifically about Shakespeare expressing how unique and special his Lady is, and how her uniqueness will never fade so long as the sonnet about her (this one) exists.
One has only to read the sonnet to realize that Shakespeare's purpose is quite the opposite of attempting to insult her. He glorifies her, saying that she is more lovely than mere forces of Nature and that her loveliness will outlast these ephemeral things, precisely because it has inspired these poetic lines, which will exist for all eternity. So long, that is, "as men can read and eyes can see."