Fighting for animal liberation and an end to speciesism
I’ve seen this claim before, and I assume that when they say “choose” they are speaking in a metaphorical sense. Species cannot choose and in general individuals also do not make choices in the way implied by “chose domestication”.
Domestication involves changes in temperament, behavior, and morphology which result in an adaptation to being exploited by humans. Such changes are caused by selection between behavioral differences stemming from genetic and/or cultural variability.
In other words, those animals who displayed a greater tolerance for human proximity and (later) for increased human manipulation had more surviving offspring. Maybe the human presence provided protection from other predators.
It works both ways. Those humans whose exploitation of animals became more systematic and (later) more directly manipulative also had more surviving offspring.
In both cases there is evidence that the average individual did not have a better life as a result of domestication. Humans in agricultural societies were smaller and had more disease than their pre Neolithic forebears. Likewise domesticated animals seem to have become smaller and less robust over time. However, the significant point is that the arrangement gave all participants a procreative advantage and that in biological terms is success.