Great caution in gender segregation is praiseworthy
Concerning your question whether to establish a girls school in [the city of] Michnaz, this is certainly proper, and not just in Michnaz, but also in other places. However, one must be particular that they not be together with the boys. This means that not only should the boys and girls not learn in the same classroom, but the school should be built such that each gender enters and leaves from a separate entrance. Furthermore, it is preferable that the two schools be housed in separate buildings and streets, for the greater the caution in such matters, the more one is praiseworthy.
Igros Kodesh, Vol. 6, p. 33.
All schools require segregation
I emphasised that my demand for the principle of segregation in Chabad institutions is not exclusive to Chabad institutions, but my opinion is clear that the same applies to all schools. In this lowly, orphaned generation this is not merely a religious question but also one of ethics and modesty in the most simple sense. This can be seen in the institutions where this principle is not practised, where the disastrous consequences have increased to such an extent that despite every effort to conceal them and prevent unpleasant publicity, from time to time they break out and become communal knowledge.
Igros Kodesh, Vol. 14, p. 434.
Single-sex education is equally necessary for non-Jews
... This is not a matter exclusive to the Jewish religion, (although that alone should be more than enough) for in recent years gentiles have also begun to see the harm of mixed schooling. The alarming situation is well known to the teachers of these schools, but for understandable (though unacceptable) reasons it is hushed up. In any case, since ultimately the main thing is to fix the actual situation, [in your case] this matter could be approached differently. By increasing the number of students there will be a need [for a division of classes and] a new teacher, or at least an assistant teacher, and it is possible that if they sense that one is aiming for segregation, and for the above reason [i.e. the need for a division of classes], they will turn a blind eye to the true reason, for there will be an opening for an honourable retraction.
Igros Kodesh, Vol. 16, p. 284.
Single-sex education is an universal ethical and educational imperative
In reality, segregation is not merely a question of religion, but also an ethical and even an educational one, to which the heart readily consents, for the staggering devastation caused by co-education is well-known from an ethical and even a basic educational standpoint. The student’s attention is distracted from his studies, impinging on his academic progress ... With the appropriate and persistent explanation, those who have the ability to correct this matter can surely be convinced to do so ...
A man is compared to a tree. Just as even a tiny scratch in a soft sapling can cause a deformation in a large tree, so is it with a child. Thus alacrity is particularly needed in matters of education.
Igros Kodesh, Vol. 17, p. 29.
Segregation should begin from the youngest age
... It is primary and important that I see that your work is dedicated to educating girls in particular—meaning to say that you maintain with all firmness necessary the segregation between boys and girls in their education.
Here is an article that proves just how much boys' performance is affected by being around girls (although it is speaking about adults, the same surely applies to teenagers): Women do make men throw caution to the wind, research confirms