Why do you think Abbey wants to own Moon-Eye?

Once he learns of the reasons for Moon-Eye's isolation, he feels compassion for him and wants to help him. One might also remember Abbey's expressed wish to "own" everything that was around him so that he could feel a part of it all. Abbey also feels that horses are gregarious, and this isolation is not a natural state for a horse. In a sense, Abbey is trying to make things right with nature with respect to this poor horse.