It depends on what you mean by fate. I could say that God knows all of the Future, and you couldn't disprove that...without disproving God.
You've got it a little backwards, because you can't prove God. But it was fair to ask for clarification. By fate, I refer to predetermination of the universe. That is to say, that given perfect knowledge of one moment of the universe, and it's laws, one could derive the rest of the history of the universe perfectly. That everything that has and will happen were predetermined thusly at the beginning of the universe.
However, due to the behaviour of particles, this is not possible. Not only is knowledge bound by the Uncertainty Principle, but even with perfect knowledge of a given state, one cannot absolutely predict the subsequent state of a given particle. And there are a lot of particles. So there is no fate.
So I reject the notion of fate, not just on philosophical grounds, but on phyiscal grounds. Belief in fate is contrary to known physical laws.