I believe students benefit both from consistency and from new experiences. It is important from the student's perspective to have a consistent instructor who knows where they are in flight-training, and what they are capable of. But no two instructors teach alike, and it is important to get different view points, information, techniques, etc.

In my training, I've had the same instructor most of the time. But occasionally he's unavailable, and I end up with a substitute. Each sub has definitely had a subtly different, but new approach to flying the airplane, and I end up learning something new.

In this sense, I do have "my" instructor, and I am "his" student. But I don't think he'd have any problem with me occasionally flying with someone new. If I were to switch to a different instructor as my primary CFI, he might well wonder why, and maybe even take some personal offense.

But there is another important angle, the student-as-customer. Obviously a student wants a teacher who fits them well, and I know I've met at least one instructor I wouldn't get along with long-term. For one lesson, it was fine, but for an ongoing project, I would have sooner quit. If the student doesn't feel right with an instructor, I absolutely support them finding a new instructor. But hopefully this is done early enough before one instructor starts to feel they "own" the student.

I know an instructor might not enjoy losing a student, but it should be viewed a bit the same as a salesman losing a regular customer. It is business: each has their own interests to look out for foremost, and losing a customer may sting a little, but it shouldn't be a big deal.