I'm often pretty skeptical when it comes to Proto-Afro-Asiatic and cognates that are proposed for it. There are many great morphological similarities between the Afro-Asiatic languages.
The lexical items that are reconstructed only seldomly manage ton convince. All too often Afro-Asiaticists will reconstruct some word back to Proto-Afro-Asiatic from some extremely marginal words in the specific branches, while making no distinction between reconstructions that are really widely attested and easily reconstructed for the specific Proto-Branches and those that are not.
The amount of chance correspondences when allowing so many option is enormous, and basically useless.
For a Afro-Asiatic comparison to be believable at all, it should at least be broadly attested in the whole language family. Too often I've seen comparisons between Tuareg (a very innovative and lexically divergent Berber language) and a single Semitic language, which then receives a reconstruction for Afro-Asiatic. This will not do.
Today I'd like to do a little bit of Afro-Asiatic comparison myself! Recently I was on the opposition comittee of Richard Gravina's PhD defense. He has written a wonderful thesis The Phonology of Proto-Central Chadic. While I was reading this thesis, I actually ran into several fairly nice Proto-Central Chadic that look suprisingly much like Berber.
So below is a tiny overview of Gravina's reconstructions (which can also be found online here), with some cool very similar words in Berber (and occasionally Semitic):
PCChad. *kɨr 'to steal'; PB *ăʔḱər 'to steal';
PCChad. *mɨts 'to die'; PB *ămmət 'to die'; PSem. *mawita 'to die');
There seems to be some connections between PCChad. *t and *ts, and both seem to go back to Proto-Chadic *t.
PCChad. *ɬɨɗɨn ʸ 'tooth'; PB *e-sen 'tooth'; PSem. *sinn 'tooth'
The medial *ɗ in PCChad. would seem problematic for comparison. But it only shows up as such in very few languages. More often it is found as a y. I'm inclinded to think that this is rather the original form, i.e. *ɬɨyɨn.
What's interesting is that the lateral fricative *ɬ in PCChad. corresponds to PSem. *s. PSem. is usually reconstructed with a lateral fricative (often transcribed *ś) for example in: *śahr 'moon'. One would perhaps expect that rather the lateral fricatives would correspond to other lateral fricatives.
PCChad. *sɨn 'to know'; PB ăssən 'to know';
PCChad. *vɨn ʸ 'hut'; PB *e-βăn 'tent' (< Pre-Proto-Berber *a-bănH ?); Perhaps related to PSem. *banaya 'to build'?
PCChad. *v seems to come from PChad. *b.
PCChad. *ɬɨmɨɗ ʸ 'ear'; PB *isəm 'ear';
Once again this *ɗ shows up as y in the majority of the languages. So: *ɬɨmɨy ?
This word for 'ear' is not widely attested in Berber. Only Ghadames ésəm, Awjila ísəm, perhaps the Zenaga verb ẕ̌əššəm 'to hear' is related to it as well.
A connection with PSem. *samiʕa 'to hear' has been suggested, and may be a possible.
PCChad. *ɬɨmɨɗ ʸ 'name'; PB *iʔsəm 'name'; PSem. *ʔism 'name'
The Berber word might be an early loanword from Semitic instead of an original Proto-Berber word. Once again we find the correspondence of *ɬ and *s.
PCChad. *maj 'mouth'; PB *e-me 'mouth' (< Pre-Proto-Berber *a-may ?);
Is there a relation with Proto-Semitic *pay 'mouth'. I would not necessarily expect a PSem. *p to correspond to *m in other Afro-Asiatic languages
PCChad. *viɗ 'night'; PB *e-βăḍ (< Pre-Proto-Berber *a-băḍ ?);
PCChad. *ɗɨyɨm 'water'; PB *ama-n 'water' (Pre-Proto-Berber *a-HămăH-ăn ?); PSem. *may 'water'
Once again this *ɗ shows up as y in the majority of the languages. So: *yɨyɨm.
This comparison is admittedly a little tentative.
PCChad. *dzɨwɨɗ ʸ 'fly'; PB *izi 'fly'; (PSem *ḏubb 'fly' ?);
This final *ɗ here is *ɗ quite a bit more often than in the other examples, but for this comparison to be at all convincing it has to go back to a *y: *dzɨwɨy ʸ
PCChad. *sa 'to drink'; PB *ăswəʔ 'to drink';
PCChad. *wɨvɨn 'millstone'; PB *taʔβunt 'stone, millstone'; PSem. *ʔabn 'stone';
PCChad. *ɣʷɨr 'filed'; PB *egăr 'field' (< Pre-Proto-Berber *a-Hăgăr ?)
The Berber word is often understood as a Latin loanword (cf. ager 'field').
But even Sumerian has this word a-gàr 'irrigated field'. Appears to be some sort of agricultural wanderwort (Thanks to Lameen Souag for pointing that out).
PCChad. *ɬɨn'to send'; PB *azən 'to send' (< Pre-Proto-Berber *ăHzən ?)
Proto-Berber is a little difficult to reconstruct if Awjila əssə́n 'to send' is related. The correpondence *ɬ to PB *z has not been seen in other words yet.
PCChad. *nɨh 'to ripen'; PB *ănwəʔ 'to ripen'
PCChad. *tsɨ ʸ 'eye'; PB *t-iḍ-t 'eye'
PCChad. *v 'to give'; PB *ăkβəʔ 'to give'
Of course a comparison of a single consonant is not exactly convincing.
PCChad. *vɨn 'rain'; cf. Awjila avún 'rain'
Obviously this comparison is completely unsatisfying. The normal word in Berber for 'rain' is *amẓar, which has quite an interesting cognate in Semitic *maṭar 'rain'. Yet the isolated Awjila certainly has a striking similarity to the Central Chadic form.
Obviously not all of these comparisons are as convincing. And I would not want to actually reconstruct a Proto-Afro-Asiatic yet, but I think some of these comparisons are at least interesting to explore further.