I am so mad at Benjamin. I need to clear space in my town, and I got so excited when he pinged me. And then he changed his mind in that same conversation! Has anyone else had this happen to them?
Yes, this can happen if your friendship with that villager isn't very high.
The solution to is is just to quit without saving. Because the game saves as soon as you load your mayor, Benjamin will be scheduled in to move. So after he pings you and stops moving, you can just quit the game, restart again. Benjamin will probably ping you again, but you can just ignore him and he will move out in a few days.
I've done this plenty of times myself. If he pings you to move, then changes his mind, simply reset the game, and then find him again. He'll ping you again about moving. He may agree to move on your second try, or you may have to reset a couple more times, depending on how stubborn he's being.
In addition to restarting the game until they accept to leave, you could also just avoid them until they move out. They don't have to tell you if they're moving out, and I've often had times where I didn't realize a villager was moving out until another villager told me. If you want to TT them out after you know they'll move, just take it a day at a time, if you want to have someone pick them up, or just TT 5 days forward from the first day you find out they're leaving.