When applied to animals this space is called the flight zone. Walk into this space and the animal will move away from you. When threatened an animal's first choice is to get away - the flight response.
All mental circuits are focused on finding an escape route.
Finding an escape route is an instinctive response. The animals will be thinking and problem solving as they move. You, too, must think and plan ahead. The animal knows where to stand and where not to stand to remain safely out of reach. They are keen observers of human behavior and n othing is more important to them than being safe.