Macarius
Haili's simple know is a little short on clarity.
Let me Add:
The Ethiopian Orthodox Tewahado Church is and has always been an independent community among all other communities of the Universal Apostolic Church from the Apostolic era.
The First reach of the Apostolic mission beyond the Israelites were the Ethiopians via St. Philip and the Ethiopian Eunuch (Acts:Ch

. Ethiopians were present at the Pentecost (Read the writings of St. Dioscorus).
The point here is their is nothing new to the fact that Christianity is ancient among the Ethiopians.
What is at hand is why Egypt held bisphoric for herself and Ethiopia?
I have read this:
Egypt is the true See of St. Mark and as such her chief bishop or Patriarch is the true representative of the see of St. Mark. Ethiopia does not discredit this at all.
The Ethiopian Patriarch represents the See of St. Teklehimanot as was established by the Coptic Bishops when they administered over the Ethiopian Church. Thus the Ethiopian Patriarch has under his jurisdiction the whole See and has no other head in this See. He is supreme head of the Church of Ethiopia and the Arch Bishop of Axum.It is not clear to me but it seems that it is thought that since the Coptic Arch Bishops who held administration over the See of St. Teklehimanot 'answered' to the Coptic Patriarch in Alexandria that the newly autocephalous Ethiopian Administration (1952 or their about) now with 'Ethiopian' Arch Bishops and thus the chief of the Arch Bishops...The Patriarch who now holds the See should keep the same tradition and answer to the Patriarch of Alexandria as was with the previous Coptic Arch Bishops of Axum.....

?
This my rough assumption...
It is kinda confusing; and some of the info is not clear or specific that I have read on the subject.
But I can say that the liturgy in the Ethiopian Church mentions the Patriarch of Ethiopia and all Arch Bishops, Bishops, Priests and Deacons world wide.
It is also important to note that the Ethiopian and Coptic Church enjoy a good relationship. Our members worship together without any problem.
The Coptic Church fathers are blessing and caring for Ethiopians abroad where Ethiopian Churches are not yet established or in a very small and growing condition.
The commandment to love one another and care for one another above ALL things is the greatest commandment and is the act of true righteousness. The Ethiopian and our Coptic brothers are one in this regard (thanks be to God).
This subject deserves prayer.