Questioning Doctors due date

Hey ladies I got an ultrasound last week! According to him I am 7 weeks four days, due date September 21. I did the math and that would mean my SO and I conceived around December 22..... Not possible! haha. We looked back and thought we had unprotected sex around the 12th maybe 13th. So it's way off! We only did once, never after that. How would I have not gotten pregnant then, but somehow would a couple weeks later with protection? I'm just confused. It doesn't REALLY matter I guess. But are the doctors ever inaccurate?