Basically the game keeps track of which villagers have lived in your town and it stores data on 16 past villagers, where the 17th will replace the 1st, 18th the 2nd and so on. If the villager you want is within that 16 villager cycle, they won't be able to move into your town through any means other than scanning in an amiibo card yourself. By moving out 16 villagers, you get them out of the cycle and you can then adopt them to your town.