I don’t think Vonnegut personally believed in predestination. He was a humanist and an atheist. Since humanism asserts that people should work to benefit society, my guess is that he also believed that people had free will, since working to benefit society (as opposed to choosing not to do so) requires a decision.
Nonetheless, predestination is a major theme in Slaughterhouse Five. In fact, much of the novel reads like a debate over the legitimacy of free will over predestination. On the predestination side of the argument, there’s Harrison Starr’s theory that writing an anti-war novel is like writing an anti-glacier novel; i.e., war, like glaciers, is inevitable, so there’s no sense in trying to stop it (3). But on the “free will” side of the argument, we have the fact that Vonnegut ignored Harrison Starr’s advice and wrote an anti-war novel anyway.
Yet this act of free will — the decision to write a novel that might influence its readers to reject war — is itself haunted by doubt, as exemplified by the Tralfamadorians’ understanding of time and space. The Tralfamadorians, we learn, find free will to be a foreign concept because they see the past, present, and future all at once (86). At the same time, though, there’s something terrifyingly absurd about that vision: they know how the universe will end, and they don’t do anything to stop it. From their perspective, it had to be done.
Professor Rumfoord, the military historian, echoes this sentiment when he tells Billy that the bombing of Dresden “had to be done” (198). Of course, the fact that it’s Rumfoord telling us that it had to be done — and that Rumfoord is described as “a hateful old man–conceited and cruel” suggests that we’re not supposed to agree with him (193). That Billy stands up to Rumfoord by saying “I was there” suggests that he’s exercising some degree of free will, just as Edgar Derby exercises free will when he stands up to Howard Cambpell elsewhere in the novel.
I’d also argue that Vonnegut’s concerns over free will can be seen in the idea that Tralfamadorians see humans (and all creatures) as machines (154). I want to complicate this image a little bit by suggesting that we can replace “machines” with “computers” or “robots,” and that the actions of the kinds of machines we are (in Vonnegut’s view) are therefore dictated by software or a kind of code. In other words, while some things are hardwired into our physical makeup (e.g., instincts), something else is responsible for the decisions we never really think too much about. That “something else” is the set of cultural norms and assumptions into which we’re born (comprised of many things, like myths, religion, manners, attitudes, and unspoken rules).
This “software” (our assumptions) causes us to see the world in a certain way (or frames our perceptions). Building on the idea that Vonnegut is not in a position to judge his characters as good or evil (or as heroes or villains), he’s basically recognizing that each character’s definition of “good” or “true” hinges on the “software” that his or her culture has been installing since birth. Thus Billy doesn’t judge Rumfoord’s assessment that “It had to be done” because that assessment is “true” to Rumfoord based on everything he’s ever read or been taught to believe.
The challenge that Vonnegut poses to us, I think, is asking us to recognize that even if we are machines, we have the capability to reprogram our software. In other words, by writing a book like Slaughterhouse Five, he’s saying that once we recognize the cultural assumptions that dictate many of our actions, we can question and eventually change those assumptions in a way that will allow us to avoid the fate of the Tralfamadorians.