When using a filter to remove array elements, you need to use the PullFilter
builder instead of Pull
(which matches whole elements).
var collection = db.GetCollection<Person>("people");
var filter = new BsonDocument("username", "bodrum");
var update = Builders<Person>.Update.PullFilter("followerList",
Builders<Follower>.Filter.Eq("follower", "fethiye"));
var result = collection.FindOneAndUpdateAsync(filter, update).Result;
Or somewhat more succinctly, using lambdas:
var update = Builders<Person>.Update.PullFilter(p => p.followerList,
f => f.follower == "fethiye");
var result = collection
.FindOneAndUpdateAsync(p => p.username == "bodrum", update).Result;