A Brief Description of the Question:
In the verse, the following is said “He who taught (the use of) the Pen―”; however, do teachers not teach this at schools; will you please explain the relation or difference between them?

The Answer:
The related verses are as follows:
“Proclaim! (or Read!) in the name of thy Lord and Cherisher, Who created―
Created man, out of a (mere) clot of congealed blood:
Proclaim! And thy Lord is Most Bountiful―
He Who taught (the use of) the Pen―
Taught man that which he knew not.” (al-Alaq, 96/1-5)

These verses are the first revelation that was given to the prophet Muhammad (PBUH) and it orders the Prophet and all Muslims to read and encourage them to write with pen and progress in sciences. The first revelation starts with the order, “read” and the repetition of that order twice shows how reading and science are important in the life of man and religion. It is significant that Qur’an defines the difference and superiority of human among living things with his characteristic of learning. (see al-Baqara 2/31)
When Jibril (AS) asked the Prophet Muhammad (PBUH) to “Read”, He answered, “I do not know how to read” by thinking that reading can only be performed by literate people. So, the third verse is an answer in a sense for the indirect excuse of the Prophet (PBUH). So, according to this, God’s grace is infinite; He created man from “Alaq” (the Zygote) and made Him a perfect living creature and raised him to a great position like prophethood by His (Qudrah) power as He is able to teach some of His slaves as He wishes from usual ways; that is, letting them to learn from a teacher by using pencil and other tools for learning but He also has the power to teach some of His slaves that He wishes without a teacher or a learning tool.
In the 4th and 5th verses, the importance of pen is emphasized since there are many great benefits in a pen. With the help of pen, sciences are taught, wisdoms are recorded, and previous events were written. Divine books were written; in short, civilizations gained continuity and were transferred from one generation to another; God taught man what he did not know, saved him from the darkness of ignorance and let him embrace the light of science.
When the function and aim of “pen” are considered, it is necessary to say that this covers all reading, writing and information gaining tools from pen to computer. (See. Kur’an Yolu, Committee, the interpretation of the related verse)
So, it is God who teaches writing with pen and lets man have the knowledge of science. Otherwise, man, who was created from cloth, can know neither the pen nor writing.
Accordingly, every teacher undertakes the duty of the pen.
On the other hand, it is possible to understand the verse, “He taught man that which he knew not” as He taught man by creating the powers, talents and abilities, by showing evidence and by sending verses as a divine gift and also as He taught man to obtain things through working. (see Elmalılı, Hak Dini, the interpretation of the relevant verse)