Confused about calculating due dates

According to this Pregnancy Calculator, I am 13 weeks and 5 days pregnant. The American Pregnancy Association states that the first day of pregnancy is counted from the first day of your last period, since it is often difficult to pin-point the exact date of conception. Let me tell you why this bothers me. I know that I did not get pregnant on the first day of my last period… It must have been a couple weeks after that. My last pregnancy went 2 weeks beyond my calculated due-date.  According to the hospital procedures where I gave birth, 2 weeks over-due means you get induced. And getting induced is not fun. So if my due-date was really not when they decided it was, that means I was induced for, um, no good reason! I went in for my monitoring and ultra-sounds (every other day… so annoying!), there was plenty of fluid, little Esther was perfectly safe and sound, she simply had no intention of going anywhere just yet. And who can blame her, when this whole due-date calculation makes no sense?? Is it just me?