Why do people think there is a contradiction between free-will and determinism?

The concept of determinism is that, since everything is mathematically pre-determined, you have no other choice but to do what you do. For example: you might think you chose to have cereal this morning, but really, since every single atom in the universe moves only according to the forces that act on it, those atoms must move a certain way -- including the atoms in your hand that poured a bowl of cereal. Since everything is a chain reaction back to the beginning of time, you could not have had toast for breakfast even if you wanted to (but of course, you wouldn't want to, because the atoms that make up the chemical reactions in your brain are subject to the same forces, etc.) Some people think that a choice made, when nothing else could really be done, doesn't count as a "free" choice, while some do. It might be that you "chose" to do everything you do, but your state of mind leading to your "choice" is pre-determined. Am I correct in thinking it is your view that, if you would have chosen to do it anyway, that makes it a free choice of yours, even if you could not have chosen otherwise? Because that is one of the proposals put forth by compatibalism.

Humans can be both predictable and unpredictable. Like most species, we respond on an instinctive level to most of our environmental stimuli. Part of our daily activities, our mood and our responses to stressful situations, can and will be determined by various factors, depending on your nature and self-control. If one would so much observe the behavioural responses of one person to certain stimuli, he might notice a repeating pattern that could render him the tools of determining future decisions regarding that person. But that doesn't give him a 100% foolproof technique, as people may respond differently in similar situations and vice-versa. Free-will is pretty much overrated. Yes, we do have a choice between taking a plane or a train, eating fast-food, at a restaurant or cooking home, stealing or being an honest citizen, living or taking our own lives, or even the lives of others. But the multitude of choices is most of the time reduced to one, as you will choose what you usually do or like, what your instinct tells you (or what your wallet allows you for that matter). To take advantage of the full capacity of free-will you have to leave your confort zone, which, to most of us, is a "too much of a sacrifice".

What do you mean by "free will"? "Choosing your actions"? In which case, what do you mean by "choosing"? The ability to predict in advance what you then do. (No contradiction) Or the ability to, ex post, have actually done something different from what you did do. (Contradiction)