Well if it makes me look ignorant, I'm in good company, as a lot of other doctors site the same contradiction.
Other doctors? Does that mean you're a doctor? Who are these other doctors who make such an elementary mistake? Are they doctors in a relevant field such as physics or biology?
Why don't you just enlighten us with some important points from your lovely link?
Would it be too much trouble for you to read it?
Anyway, here's a summary: Entropy must increase over time, but only within a closed system. The earth is not a closed system. Entropy may decrease - and order may arise - locally, as long as overall entropy increases.
If the link I provided was too complicated, here's one describing a system in which entropy can be seen to decrease over time, and order spontaneously arises. What's more, the experiment is so simple you can even do it at home.
http://www.lecb.ncifcrf.gov/~toms/rockcandy.html
If you want to continue arguing, I suggest you do a little bit of research.