Ok, to understand why utilitarianism is fundamentally flawed it's easiest (I think) to look at the trolley problem.
Trolley is going to hit the 5 people, you're at the switch, do you make it hit the 1 person? I doubt Sam Harris would argue that it maximizes the most good to let it hit the 5 people (although I could make a case for both sides on that). If you're a utilitarian at this point you usually throw the switch and have it hit the 1 person. In other words, it is ok to sacrifice the few for the sake of the many (maximizing the greater good). Lives here are the objective function, and most lives = most good.
So what if I told you that the 5 are all convicted murders and the 1 is a nobel prize winning scientist? Change your mind? Where's the greater good now? If your mind is changed, what if those 5 were not convicted murders, but instead were mentally handicapped. What if they were fast food cooks? What if they were truck drivers? What if they were software engineers who had just been laid off? Gainfully employed? One of them was convicted of shoplifting. 2 of them have kids. 1 of them beats their kids. How are you throwing the switch (or not) in each one of these cases?
If you didn't change your mind, let's say it was only 2 convicted murders... who had the death sentence tomorrow... and who had threatened to kill you and your family...
From a human rights perspective, this question is easy. From a utilitarian perspective (which is what most people try to adopt when they're first introduced) it is an absolute nightmare. Try to weigh the contribution of the artist against the engineer. The musician against the businessman. The wall street investment banker against the corner baker. The life of someone who employs 2000 people against a mother of 4.
Every single time you invoke utilitarianism you have
impossible choices to make.