On the iPad in particular, I find myself wanting to flip through the pages like a book. The GUI looks like a book, so it seems natural to want to simply flip through the days. Sure, clicking on the calendar days works, but it’s not as natural?
Yes, I keep doing it as well. Very cumbersome to go to calendar and click each day.
Exactly!
Given the GUI, this seems like the most intuitive way to move from one day to the next. While pressing the day on the calendar works (and should continue to do so), turning the page seems most natural. I keep trying to do it, much to my annoyance.

Absolutely! Would really finish the look and feel.. especially on iOS!