What is the etymology of the word "ummi" (unlettered)?

Imām Ibn al-Jawzī (d. 597/1201) summarized the scholars' opinions in his book "Zād al-Masīr" as follows:

1. The unlettered person is called ummī because he is in the default state of the nation (ummah) which did not learn reading and writing, so he remains in his original state. [Al-Zajjāj]
2. He is referred to as ummī because he is attributed to his mother (umm), as writing was more common among men than women. Another suggestion is that it denotes remaining in the state in which his mother gave birth to him.