Defecation is one of the times in an animal’s life when he is at his most vulnerable. He must posture to perform the task and because of this, he is not in a position to readily fight or flee. In fact, it would be rather difficult for him to defend himself or to escape danger while he is eliminating. Your dog is instinctively aware of his defenselessness.
But your dog also knows that she is a part of your “pack”. You are a member of the family group. If your dog watches you during this time, it is because she is depending on you to give her a body language signal or “heads up” if she should be afraid. She may also be looking to you to possibly defend her should the need arise. If you suddenly leap away, you can bet your dog will respond also.
Likewise, some dogs will not defecate with anyone watching (or on a leash). Perhaps he feels safer if he is away from your home turf where he will not draw attention. Instincts dictate your dog’s reaction to his own helplessness during this awkward time.
Whether your dog looks to you or slips away for “poop time”, it helps to know that she is just doing what comes naturally to her. You should honor her wishes as long as it is safe to do so. Try not to do anything that will startle her if she is looking at you while she defecates. Respect her natural inclination to be away and modify your environment to accommodate her as much as possible.
Source: http://iheartdogs.com/ask-a-vet-why-does-my-dog-stare-at-me-when-he-poops/
