A new study on East African population genetics argues that it supports the finding that the Afro-Asiatic languages (e.g. ancient Egyptian, Hebrew, Arabic, many Ethiopian languages (from multiple Afro-Asiatic language families), Hasua, Berber), have a Northeast African rather than an Levantine origin.
The Essence of the Afro-Asiatic Urheimat Debate
The analysis that goes into resolving this ancient question of historical lingustics is quite involved.
The biggest argument for a Levatine origin for these languages is that language families have tended to expand with the migrations of the first farmers. Farming undeniably arose in Jericho in the Levant, a thousand years or so before it spread to Africa, most notably in the civilization of ancient Egypt. The Egyptian Neolithic revolution involved domesticated species of plants and animals that mostly derived from the Fertile Crescent Neolithic (the donkey is an Egyptian domestic exception that proves the rule). Historically, although far less so these days, the Levantine hypothesis carried with it notion of Eurasian racial superiority relative to Africans.
The biggest arguments for an African origin of the Afro-Asiatic languages are that all but one of the six major sub-families of the Afro-Asiatic language family were exclusively African in geographic extent at historically known points in time (the six families are Semitic, Coptic, Berber, Chadic, Cushitic and Omotic). The expansion of Hebrew and Arabic beyond Southwest Asia are historically documented phenomena.
African has greater historic linguistic diversity within the language family than Southwest Asia. Also, the Levatine branch (Semitic) does not appear to harbor any genetic component shared by all Afro-Asiatic language family speakers, while Semitic language speaking populations do have some African genetic component. This last point is underscored by the latest study. Many supporters of African origins for Afro-Asiatic languages are motivated more by an ideological commitment to Afrocentric perspectives than by the strong but not unequivocal linguistic, genetic and archaeological evidence that supports this perspective.
It doesn't help that there is no linguistic consensus on the relationship of the six major Afro-Asiatic linguistic families to each other. Genetic arguments are complicated by differing patterns of paternal and matrilineal descent in the relevant populations.
The only real point of consensus in this pitched debate on matters that aren't historicallly documented is that the Ethio-Semitic languages have a common Levantine origin in a single Semitic proto-language sometime near the boundary between when ancient history and prehistory meet, and that the local ancestors of the Ethiosemites spoke some manner of Cushitic language.
But, the Ethio-Semitic layer genetically may have been thinner that early estimates looking merely at Eurasian and African contributions to Ethio-Semitic population genetics would have suggested, because many Cushitic populations also have substantial Eurasian genetic components.
More Complex Scenarios
The trouble with all of the simple arguments is that they may oversimplify a complex process.
For example, it could be the case that Egypt received agriculture from the Levant substantially via technology transfer that included a mass language shift, rather than by demographic replacement, and that other Afro-Asiatic languages derive from an ethnically Egyptian Neolithic expansion. In this scenario, for example, Semitic languages might be Egyptian derived even though Egyptian itself could have a Levantine origin; in this scenario Chadic and Cushitic respectively might be Blue Nile and White Nile offshoots of ancient Egyptian (a.k.a. the Coptic language) speaking pioneers. A Levatine pro-Afro-Asiatic language might be lost entirely, replaced by a backmigrating wave of Afro-Asiatic language speakers who transmitted the Semitic languages.
Populations that are linguistically Berber are a quite pausible case, given their genetic makeup, for genetic continuity despite language shift to an Afro-Asiatic family language.
Linguistically Chadic populations, in contrast, are quite genetically distinctive, for example, having high frequencies of Y-DNA haplogroup R1b-V88, relative to neighboring non-Afro-Asiatic populations and relative to other Afro-Asiatic populations. Their relative lack of admixture with neighboring populations until the 20th century suggests a fairly recent origin for this language family relative to other Afro-Asiatic language families.
Linguistically Omotic populations (the smallest of the major Afro-Asiatic language families) could conceivably have arisen from areal influences and creolization between Cushitic speakers who border them on the East, and Nilotic language speakers who border them on the West.