I still don't get what you don't understand after reading the thread twice? The point about people cycling is that they want their town to be a certain way. Some people, e.g. Jimmy, are very particular about their town and want things placed in specific places. They also want specific villagers to either fit their town theme or are their dream villagers, etc.
So Jimmy wants Phoebe to be in his town. He also does NOT want her in front of his house, in front of the town hall, crushing his hybrids, crushing his perfect fruit trees, blocking his campsite, etc. etc.
Jimmy forgets what day Phoebe is moving in on, and accidentally loads up his mayor. Phoebe roped off her plot on one of the locations Jimmy doesn't want her to plot her house.
So if he:
i) wants to keep Phoebe and
ii) doesn't want her in the place she currently is
he HAS to cycle out 16 villagers. There's no other choice if he wants both those things.
A lot of people I see this happen to either suck it up for a favourite villager, or move them out if they can't handle their location.