Every villager has a 1/333 chance to move into your town (not counting WA villagers). You start out with 5 villagers, so right of the bat you get a 5/333 chance to get your favorite villager (for example, when I reset my town back in August, I got Fang, who is a dreamy of mine). But after that, you only get a 1/333 chance for a villager you love to move in (unless you have an amiibo card). All chances are equal and random.
Stitches, like any other villager, is not rare, but a lot of people want him. There's not enough of him to go around, because not everyone gets him... does that make sense?
I have to agree with Jon_Snow here; I'm not a big fan of Stitches. Don't get me wrong, I'm a fan of the lazy villager type, but he kinda... creeps me out, lmao. I prefer Derwin and Drago as the lazy villagers in my town.
If you don't want him, you can always go to the Villager Trading Plaza to get rid of him. I'm sure people are willing to pay TBT or IGB to have him
But if you DO want to keep him, that's great! I'm glad you found a villager you like!