Well, I suppose we are going to have to look at the throat first
There have been cases of Diphtheria in school
If I don't check your throat you could die!
As the doctor started to go towards the little girl to check what is wrong with her throat, he noticed that she gave him no expression to him and looked at him with "her cold, and steady eyes". Off the bat we notice that it's not gonna be easy to check what's wrong with her because she gives signs that she will put up a bad behavior. You can see how this leads to the conflict.
On the tonsil's! it's covered with membrane
The doctor started wondering what actually is wrong with her throat and the parents say that diphtheria has been going around her school lately. Knowing that, he wanted to look at her throat to make sure she is ok because she could potentially die from it. The little girl is still showing no emotion. The doctor tried to be nice and careful with what he wanted to do but she wouldn't let him because she is scared.
At this point, her parents are disappointed in her behavior to the doctor and they are obviously scared that she could die. Her dad holds her back while the doctor tries to check what's wrong and she still keeps fighting back and the doctor gets mad because he doesn't want her to die.
Both parents were in shock when she started turning the wooden spoon into splinters which made her mouth bleed. The doctor didn't care because she was the one who did it to herself with her bad behavior. All he wanted to do was to make sure she gets rid of her sickness that could kill her. Once the doctor noticed that it wasn't going to be easy, he knew he had to get it done somehow.
The doctor finds out that she had been keeping a secret from her parents that she is sick which also disappointed them because they didn't know that their child was in danger this whole time. So they have a right to be mad at her for not telling anyone.