The assumption that a computer couldn't feel emotion is essentially a Physicalist prespective. Type physicalists think that every emotion corresponds to a certain structure and state of being in the brain, a specific structure of neurons activating in a specific pattern. This is derived from the fact that we know changing the state of your brain changes the state of your emotions and the other way around, so it seems reasonable to think that the brain state and mental state are in fact the same thing. If this is the case, then a computer can't experience the same emotion we can, because it doesn't have the capabilities of having the same brain-state. This doesn't necessarily preclude a computer having a mind, just human emotion.
As a side note, a large number of philosophers and neuroscientists are Functionalists, meaning the function of the mental state, not the corresponding brain state, defines the mental state. Anything that serves to warn of bodily damage is pain, not only C-Nerves firing in the human brain. I prefer this because Physicalism has some alarming implications, such as that animals cannot feel "pain" the way we can.
An emotionless being is so terrifying because the human concept of morals, in the everyday sense, is largely if not completely based on empathy. Empathy is a key trait in all species that successfully work in groups, especially pack animals, because it allows creatures to naturally look out for each other. When a person feels that something is wrong, it is often because they can imagine how the wronged person feels, and replicating that emotion makes the observer feel bad and want to fix things. Since this is our deeply ingrained way of understanding morality in a heuristic day to day sense, it's a natural conclusion that a machine incapable of emotion, and therefor empathy, could not have ethics in the way that we do.
