Oh, I get it.
If you tap once anywhere on your list, you enter "Edit Mode." (Indicated by the word "Done" in top right corner.) If you then press, hold, and drag the circle next to a given list item, it will always be duplicated – no matter how long you hold it, or how hard you press it. (Out of frustration and blossoming anger, no doubt.)
If you do not tap your list first, I guess you're just in "View Mode" or something. (Indicated by the absence of the word "Done" in top right corner.) In this mode, you can check and uncheck list items, but not type anything. More importantly, when you press, hold, and drag the circle next to a list item, it will be moved instead of duplicated.
I can kind of understand the logic here, but still; thinking of the amount of time and energy I have wasted deleting duplicate lines fills me with a rage so potent it could charge my iPhone for a year.