I have taken a lot of pictures of birds over a long period of time and it is nearly always a challenge. Most of the time the birds notice that you are around, and for some reason or another they do not like to have the wide barrel of a zoom lens pointed at them. Their response is usually one of wariness, and some birds are more skittish than others in this regard. So taking a picture of of a bird requires a lot of quiet, a little bit of stealth, an absence of any kind of abrupt movement, an infinite patience, and a good zoom lens. You take your chances and sometimes you are successful.
Since most birds I encounter have eyes on the sides of their head, they can see you even when they are not facing you. You do realize that the bird is looking at you, most often because the bird will in all likelihood react to your presence in some way. It does not seem unnatural to you that the bird has not turned its head towards you. I am guessing that there is no depth to the image of you that the bird is processing internally in this scenario.
But there are also some occasions when the bird will actually look at you, or try to look at you, straight on. It will either turn its head towards you or it will seat itself in a position facing you. I wonder if the bird is getting a better stereo vision from this position, and whether there is something that induces the bird to face you from a certain angle or the other depending on the circumstances.
Finally, there are the birds whose eyes are in front of their head. I think they may have no choice but to face you when they want to look at you.
I imagine that these types of behaviors of different kinds of birds are a result of evolution and of changes that have taken place over a long period of time. It would be great to understand why certain species developed in certain ways and how it might all be related to their survival in some form or the other. Fascinating stuff! Too much to learn in too little time!