Recently it seems every five seconds(not literally)a villager is talking about moving. I have ten villagers, but I have a perfect town rating and I do talk to them. Why does everyone want to leave?
What makes villagers want to leave is having a high level of friendship. Friendship is a mostly invisible measurement of how happy your villagers are with you. Doing things like running errands for them, writing them letters with or without gifts attached, and saying nice things about their house while visiting are all things that positively effect your friendship with a villager. Eventually, when near its highest levels, this can result in things like villagers coming over to visit your house unannounced, inviting you to sit next to them on a bench and smiling if you do so, and giving you their picture.
Unfortunately, that's just how the game works. In a bittersweet twist, the closer we are to our villagers, the more likely they are going to be in wanting to leave. Perhaps this was intended so that players spend lots of time with their villagers and cycling them out with other villagers, but more often it seems that people are disappointed that the villagers they want to keep want to leave while the ones they don't want to keep are less likely to request it. If so, it's one of those things like grass erosion that is probably a better concept in theory than in practice.
Also, that's just a thing that happens when you have 9 or 10 villagers, the town is in a move-out mode. I think 8 or lower is move-in mode, where the town will want someone new to move in. Also, having a perfect town rating has absolutely nothing to do with villagers wanting to leave.
Isabelle can be very misleading when you have perfect town status and she tells you the villagers "never want to leave". The game is built to keep moving villagers out and new ones in, so when you're at 9 or 10 villagers they will keep pinging to move. It's nothing you're doing wrong and there's nothing you can do to stop it.
Luckily, if you want to keep your current villagers, you can tell them to stay when they ping you and they will listen. But you have to keep checking for a mover every few days or someone may eventually move out. You have a minimum of 10 days to catch the mover and change their mind, though.
It's a bit of a flawed system in my opinion, but better than the old games where they moved without warning.