Mark Wilson over at Fast Co. describes the uneasiness one might feel when playing video games and seeing the dead stare of a hyper-realistic character on screen. It's a straight shot into the uncanny valley if you've ever played a recent video game where characters are modeled after real people (in the article he references NBA2K17). As it turns out, while we can realistically render hair blowing in the wind and textures on a car, even the best of CGI has a hard time reproducing the actual likeness of the human eye. Why? Well, just like the eye, the answer is multifaceted and complex. But essentially, it boils down to how complicated the eye really is and how it reflects light so differently not just in different lighting scenarios but also from what exactly is being "seen" around the character's sight.
One step towards getting realistic eyes is by modeling them after real eyes. But even here, there's a problem because the CGI is only recreating a specific recorded scenario rather than letting the video game process what's going on in the scene and generating a completely new visual. Yeah, it's not so easy. This is a good read though.