Animal Crossing: New Horizons takes place on a deserted island where players have to turn the place into a hospitable abode for themselves as well as ten other anthropomorphic villagers. They can get these villagers from mystery islands, amiibo cards, or even villagers who simply wandered into their campsite.
If they want the villagers to reside on their island, players simply have to speak to them and convince them to stay. However, on occasions, villagers inform them that they might be thinking of leaving their island.
This happens due to several reasons, and a few of them are enlisted below.
Animal Crossing: New Horizons villagers leave due to a number of factors
1) They have stayed on the island for a very long time
One of the most common reasons why New Horizons villagers leave players' islands is because they have been on it for too long. When they think about moving, they will have a white thought bubble looming over their head, and they will appear very lost.
When interacted with, these villagers will inform the player that they believe it is time for them to move on. In such cases, if the latter wants the villager to remain on their island, they can simply try to convince them to stay by interacting with them.
Their response highly depends on their personality type, but most of them decide to respect the player's wishes and stay on their island.
2) Due to negligence
New Horizons villagers often request to leave a player's island when they have been ignored by them for a very long time. This is one of the easiest ways in which players can get rid of villagers they don't want on their island anymore.
However, apart from negligence, a player's behavior towards a villager can also drive them towards wanting to leave the island. If the player misbehaves with the villager, such as pushing them around, ignoring them, or hitting them, the latter might inform them that they wish to leave.
3) Time travel
Time travel is highly debated in Animal Crossing: New Horizons, and villagers leaving is one of the main arguments put forward by players who are against time travel.
If players travel too ahead in time, the game takes it as them being absent for that many days. This results in villagers feeling neglected and thereby leaving the player's island. This is one of the few shortcomings that time travel has in New Horizons.
These are some of the main reasons why villagers leave in Animal Crossing: New Horizons.