This is a good question. There are several reasons why the works of Homer (Iliad and Odyssey) were used in education. In light of this, let me name a few of these reasons.
First, to study Homer is to learn to read and write Greek. Some of the most beautiful Greek was penned under the name of Homer. So, if we look at many of the fragments that were found in the sands of Egypt, the majority of them were of Homer. More specifically, children were learning to read and write.
Second, Homer's work forms the basis of many of the values of Greek civilization. Hence, to educate children on things like bravery, the importance of military prowess and the seeking of glory, Homer's works are a great place to start. Moreover, there is a collective bonding that takes place.
Third, Homer can be allegorized to make important points on ethics. We see more of this in the Hellenistic period. In other words, Homer has many exempla, which can teach children about how to live and what it means to live well.