Seeing a dentist - it is not my baby?

Situation: a patient, a very young blond-hair dentist, a
witch-look middle aged nurse

Patient: doctor, my tooth is having a problem again, 2 years
ago I had a Indian dentist to put filling in it in Lxx. Now it is hurting me.

Dentist: let me see, ... we got to have it extracted out.

Patient: oh no! do you have any other method please? Like
injecting some medicine to there for me? I'd very much like to keep it please.

Dentist: I don’t have any other method, except get rid of
it!

Patient (oh, such a stupid dentist)

Dentist: you see, if you took antibiotics it only helps for
a while, say, after one week, the problme is coming back again!

Patient was hit by this words. : Ok, doctor, lets extract it
out!

Dentist was happy. Surgery was taking place...

After a while, the nurse was holding the tooth, it looked a white, intact tooth, with one side a small black spot, and the other side a bloody tissue stick on the side of the tooth.

Nurse: look, your tooth, it is a very bad one!

Patent: where does it show? here? (Pointing to a black spot)
Nurse: pointing to a blood tissue alongside of the
tooth) There!
Patient: (unknown the situation kind just ignorantly nodding
her head) oh, can I keep it please? It is part of me,
like my baby :)

Nurse and Dentist becoming very nervous: NO! You don't need
to! It is a bad one. With bacteria.

Patient: so it is not my baby?

Dentist (laughing) No, just throw it!

 Question taking away: why does the dentist/nurse not
like the idea to let the patient take her tooth?