Albus Dumbledore was in quite a predicament, you see, his Muggle Studies teacher had vanished, rather abruptly during the NEWT examinations, and it was now well into July, and he simply couldn't run a school when one of the teachers was missing. He thought about, and thought about everybody he knew that had connections with the muggle world, deciding that even though they might suffer prejudice, a muggle or a squib would definitely be the best person for the job. After considering all the muggles and squibs he knew, which wasn't all that many, he realized that he knew the perfect person for the job, and penned a letter with a twinkle.
Dear Petunia Evans,
I am most sorry that I was not able to offer you a position as a student at my school, Hogwarts school of Witchcraft and Wizardry, which your sister Lily Evans, soon to be Potter, attended. Now, however, something has come up that I am sure you will be able to do, and I hope that you will want to. Although you were never able to come to Hogwarts as a student, as, students require magic, and you did not have any, for what I am proposing you will not need any. Hogwarts needs a muggle studies teacher. We teach muggle studies so that wizards do not become ignorant of the other society that exists alongside us. Our current teacher for this subject has just retired, and, I personally think, that, being a muggle, you would be perfect for the job, especially since you have a bit of experience in the wizarding world, and, a relative there. I hope that you will accept this offer, if you are interested, send a reply back with the owl this letter came with.
Thank you,
Albus Dumbledore
Headmaster of Hogwarts school of Witchcraft and Wizardry.
Head of the Wizengamot.