With the full control that players have on Animal Crossing: New Horizons, they have free reign to move villagers out as they please.
Below, you can find a guide on moving villagers out of your ACNH island and all the different methods to do so.
How to Make Villagers Move Out in ACNH
Moving villagers out of your island is a very important for ACNH players that want to keep the game feeling fresh.
There are multiple ways to remove villagers from your island, whether that's through time travel or no time travel.
How to Make Villagers Leave Without Time Travel
1. Decide which villager you want to move out
While playing ACNH, you can find random villagers waiting with a thought bubble.
If this goes ignored, there's a chance it'll transfer to a random villager.
2. Speak to the villager with the thought bubble
The villager will talk to you about wanting to move. If you want them to leave, encourage that they leave.
There's a chance that the villager will then disagree with you and take you wanting them to leave negatively.
3. If the villager agrees, they will prepare to leave
The next day, you'll find the villager in boxes in their home. This means they will leave the following day.
How to Make Villagers Leave with Time Travel
4. Decide which villager you want to move out
5. Skip ahead 15 days
This can be done within the system settings by changing the date and time.
6. Check island to see if a villager has a thought bubble over their head
If this isn't the case, repeat step 2 until you can find a villager with the thought bubble over their head.
7. Check to see if it's the villager you want to leave
If it's not, you can set the time back to 4:59 AM. Villager thought bubbles reset at 5 AM. Once that happens, exit the game and go back to 1 PM on the same day. Check villagers again.
8. Encourage the villager to leave
Once you've done that, the next day, the villager should be in boxes and ready to move out.
Making a Villager Move Out with the Campsite
Making a villager move out with the Campsite can only be done if you have 10 villagers, and can only be used to replace a villager.
The Campsite will not give you a vacant house spot.
9. Wait until you have a villager at the Campsite
The Campsite villagers are completely random and based on chance, so it's not guaranteed that you'll get the one you're looking for.
10. Talk to them until they ask to move in
11. Let them pick a villager to move out
If it's not the villager you want to leave, quit the game without saving and relaunch until it is.
12. Agree with them, if it's the villager you want to get rid of
This same method can be done with Amiibos at the Nook Stop.