Child psychologist: Children should make it a strict rule not to talk to anyone who has ever bullied or harassed them.
School Administrator: If we implemented that plan, then none of the children in the school would be talking to one another.
Pre-think Assumption - The Administrator's conclusion is true only on the assumption that all the children in the schools are somehow indulged in bullying.

Now the choices-
(A) Students tend not to follow rules set up at the school.
This can't be inferred from the argument.
(B) There is never a good reason for a student to bully another student.
This can't be inferred from the argument.
(C) For any two students, at least one has bullied the other at some point.
Correct. We need to assume that all the children in the schools are somehow indulged in bullying.
(D) There exists some way to prevent bullying.
If the bullying is prevented,then the Administrator's conclusion will not be valid.Administrator just questions the plan that suggests to stop the talks and doesn't bother if the bullying can be controlled or not.
(E) Bullying is the biggest problem among students at the school.
Does not impact conclusion.Cheating could be the bigger problem than bullying.So what?It doesn't matter.

IMO C

Child psychologist: Children at school should be taught to simply ignore students who are taunting or bullying them. In fact, children should make it a strict rule not to talk to anyone who has ever bullied or harassed them.

School Administrator: This is a terrible idea. If we implemented that plan, then none of the children in the school would be talking to one another!

The school administrator’s response to the psychologist relies on which of the following assumptions?

(A) Students tend not to follow rules set up at the school. Incorrect

so administrator has no reason to concern for this matter, against administrator

(B) There is never a good reason for a student to bully another student. Incorrect

there can be some good reason, extreme

(C) For any two students, at least one has bullied the other at some point. Correct

can be an assumption of the administrator

(D) There exists some way to prevent bullying. Incorrect

against administrator argument

(E) Bullying is the biggest problem among students at the school. Incorrect

support administrator argument but cant be an assumption

Child psychologist: Children at school should be taught to simply ignore students who are taunting or bullying them. In fact, children should make it a strict rule not to talk to anyone who has ever bullied or harassed them.

School Administrator: This is a terrible idea. If we implemented that plan, then none of the children in the school would be talking to one another!

The school administrator’s response to the psychologist relies on which of the following assumptions?

CP: Don't talk to bullies.
SA: Terrible idea since then no one will talk with each other.

What are the assumptions? --> Everyone has bullied everyone.

(A) Students tend not to follow rules set up at the school.
Rules? This has no bearing that someone 'bullies' another. Also, 'to bully' is not explicitly defined.

(B) There is never a good reason for a student to bully another student.
Irrelevant. This is not an assumption needed for the argument. This is a statement of fact which provides no value to the assumption

(C) For any two students, at least one has bullied the other at some point.
Right in line with our assumptions.

(D) There exists some way to prevent bullying.
This is not a key assumption since we are talking about solutions and its consequence

(E) Bullying is the biggest problem among students at the school.
Its not that it is a problem, it is that it is frequent and everyone was affected.