It was generally believed that Proto-Semitic originated in Levant and that EthioSemitic came to Ethiopia/Eritrea from there. But this claim is losing support among increasing scholars in a favor of Ethiopia origin. Why? Because:
• EthioSemitic languages are diverse. There are about 16 of them and greater language diversity shows greater time depth. At least 5000 years is needed for the the diversity like this to occur.
• EthioSemitic languages especially the Gurage branch show archaic behavior.

EthioSemitic isn’t a son of Levant&Arabia Semitic languages but a great uncle or grandfather. Proto-Semitic originated in Ethiopia and EthioSemitic was driven from this while it was in Ethiopia. Some Proto-Semitic or Proto-EthioSemitic speakers went to Arabia or Levant, and became the base for non-African Semitic languages like Hebrew, Arabic, etc.......

And also Semitic is a branch of Afroasiatic and the latter is accepted by almost all scholars to originated in Ethiopia. Same as Semitic, most of the language of the other Afroasiatic branches are found in Ethiopia.

See the works of Girma A. Demeke, Martin Bernal and Roger Blench for detail.