Domestication of animals is a cooperative activity, and cooperative activities require a sophisticated means of communication.
Conclusion (therefore)
It's likely that language developed primarily to facilitate animal domestication.
Evidence
Domesticating animals is a cooperate activity, and cooperative activities requires a sophisticated means of communication.
Evaluate
The author's evidence definitely establishes that the evolution of sophisticated language was primarily driven by a need / desire to domesticate animals.
But there are presumably other human activities that are also cooperative and would also require sophisticated communication: (agriculture, hunting, building cities, sorting out ethical rules, etc.)
Who knows which of those came first or which would be considered the primary reason that language developed?
Goal
The author seems to be treating one possible thing that could have been the driving force behind developing language as though that thing likely is the primary reason we developed language.
Or we could object by saying something besides domesticating animals was the primary / earlier reason we developed language.