If a teacher were only listening, that wouldn't be a big problem. However, many (if not most) would feel the need to actually provide advice, including advice which conflicts with the parents' wishes.
Considering the example of the girl who doesn't want to wear a hijab; simply listening to her struggles is not a problem. Encouraging her to take off her hijab at school is implicitly undermining her parents' authority. (This doesn't mean the teacher has to nag her to wear the hijab, either. The teacher should be neutral by default.)
There is no neutral stance in this case. The teacher listens to the student's concerns and asks what she is concluding. Regardless of what the student decides (I should keep wearing the hijab vs. I will not wear it in school) silence and support implies agreement.
Are there specific topics the teacher should be "neutral" about, or is it just any issue that the student has that a teacher should be "neutral" about?
The primary responsibility of the teachers is students'
education. Furthermore, the teacher should be concerned with the education of
all of the students. Anything which distracts students in the classroom from focus
on their education is bad.
Whenever a teacher is "non-neutral" about any topic on which students may have varying opinions, and varying degrees of passion, the issue will become more of a distraction for those students who are passionate about it, regardless of their opinion on it.
So, for the hijab example. By the teacher taking a side,
either supporting the student's not wearing the hijab,
or by trying to support the parents' expectation that she wear it, other students observing will be encouraged to speculate.
If the teacher supports the student in not wearing it.
- Does this mean she thinks Islam (or perhaps all organized religion) is ridiculous and/or oppressive?
- Does this mean she thinks parents are generally out of touch, and (most?) teenage rebellion is good?
If the teacher supports the parents' wish that the student wear it.
- Does this mean she thinks society is missing the authority of organized religion?
- Does this mean she thinks parents should always be obeyed, and (most?) teenage rebellion is bad?
These speculations are going to distract students,
regardless of whether they actually reflect the teacher's views or not.
By taking an explicitly and intentionally *neutral stance, the teacher reinforces the idea that her priority (and the priority of the students in the classroom) is their education.
(Sample response: "The school dress code doesn't require or forbid hijabs, so anything not part of the school dress code is not my business." Note that response is equally valid whatever "side" of the issue the teacher is on.)