Question Summary:
Why weren’t any of the Prophets (alayhim al-salam) female?

Question Detail:

I am asking these questions to further my understanding and to be able to answer other people when they ask me them (which they have), not because I disagree or want to argue them.
1.) Why weren't any of the prophets female?
2.) Why can't women work? Is it haram?
3.) If a woman works as a teacher at an islamic school, is it permissible? What about a public, secular school?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
1.) Women have historically served a very significant and influential role in advancing the cause of the Prophets and Messengers (alayhim al-salam).
If you look at the sacrifices of the blessed pious women such as the wife of Firaun, the mother of Musa (alayhi al-salam), Maryam, the mother of Isa (alayhi al-salam), Hajar, the wife of Ibrahim (alayhi al-salam), the noble wives and daughters of Rasulullah (salallahu alayhi wa sallam), and many others, you will see countless examples of leadership, sound advice, courage, teaching the female believers, calling to the faith and more.
These were vital supporting roles and the apparent wisdom behind women serving in such roles and not being appointed themselves as Prophets (alayhim al-salam) has to do with the various responsibilities that the Prophets (alayhim al-salam) had to undertake.
For example, the Prophets and Messengers (alayhim al-salam) had to invite publicly towards the faith, show miracles by the Will of Allah to the people, answer questions in public audiences, communicate with tribal leaders and rulers, mediate disputes, migrate or travel far distances in difficult and dangerous terrain, face and deal with verbal and physical opposition from hostile factions, lead the community of believers in prayer, and so on.
Many of these actions by their very nature needed to carried out in the public sphere in front of people and as a result are incompatible and inappropriate for women due to their natural delicacy and go against the modesty required of women.
A believing woman would also be committed to her home and her children, ensuring their proper upbringing (tarbiyyah). Here too, the biological differences between the two genders makes apparent the wisdom of women not being appointed as Prophets (alayhim al-salam).
For example, how could a woman in pregnancy or after child-birth deal with all the various situations that a Prophet would invariably have to face while nurturing and caring for her children? The office of prophethood, without a doubt, requires a constant commitment that far supersedes any earthly position.
All this goes to show that the position of prophethood is not suited to the nature of women, but as stated earlier, this does not mean that women have not served important roles in the lives and missions of the Prophets (alayhim al-salam).
2. & 3.) The question on women working has been answered previously. Please refer to Fatwa #19900 at the following link: http://www.askimam.org/public/question_detail/19900 and Fatwa #15865 here: http://www.askimam.org/public/question_detail/15865 
And Allah Ta’āla Knows Best
Sohail ibn Arif,
Student Darul Iftaa
Chicago, USA
Checked and Approved by,
Mufti Ebrahim Desai.