Gal(ɑ1,3)Gal (Galili epitope) is a common epitope in most animals, but in primates we lost the activity of the gene (GGTA1) to synthesise it. Since we don't produce it any more, it's recognised as foreign by our body and not only causes rejection in xenotransplantation, but also this Alpha-Gal allergy.
I'm not going to comment on the actual immune mechanisms that take place with developing an allergy to a carbohydrate epitope, beyond saying that I don't understand enough of it. Somehow we lose the tolerance to this antigen that we develop from about 6 months of life.
I'm more interested in what makes this epitope: Is this carbohydrate synthesised by the actual ticks, or is it actually something to do with a tick-associated parasite or the microbiome? Here's a review (https://pubmed.ncbi.nlm.nih.gov/31214181/) that covers this that I quickly found, suggesting that (a member of) the microbiome can in fact alter levels of ɑ-Gal from ticks.
edit: Obviously, the solution to this problem would be to just eat primate meat instead, which is one hell of a risky bet given our problematic pandemic primed populations.