Jonas's Father is a Nurturer. He takes care of babies, and, by takes care of, we mean occasionally kills them. What's so hard to understand about his character is how he can be so caring and nurturing – look at the pains he takes to help Gabriel, after all – and at the same time be so casual about unnecessary death.
But the fact is, Jonas's Father is the product of his environment. He's been trained to think that death is no big deal, just as Jonas has been trained to understand that it is. When he tells his son that his job at the release is to make the baby "cozy and comfortable," this isn't necessarily at odds with his perception of the whole event. In his opinion, lethal injection probably is cozy and comfortable. With no real understanding of pain, and no sense of the value of a human life, killing a baby is just like filling out a checkbox on his list of to-do's.
Still, it's easy to see why Jonas reacts the way that he does. Not only is his Father a murderer, but he's been lying to his son for most of his life. Jonas's rage at his father is also his rage at the entire community, for its ignorance and its disrespect for human life.