For me this means that the more you become aware of the idea of oneness and that everything in essence is you, the more you are encouraged to question the idea of owning another being, in other words to own something or even someone is to imply that it is your 'property'. 'Ownership' is possessive and implies that a person, place or thing is yours as opposed to it being a part of you, as a result it becomes difficult to integrate that part of 'source' as you can't recognise it as a part of you.
Teal mentions in one of her YouTube videos that once you become more awakened you realise that even your child/children are not 'yours' in the sense that we tend to look at our children as our property. Instead, they are their own beings who are simultaneously a part of the same 'source' energy and we (the parents) are their assigned guardians and guides assisting them with their own experience. You can look at pets the same way. She says, "The dogs of our family are members of our household..." The fact that Teal refers to them as members feels way more inclusive, like she takes them and sees them as a part of herself rather than separate. That's what I make of it.