Simple answer: Because we can't completely model our own mind. Interesting conclusion that flows from that: We as individuals will always think we have free will, but to something that comes along that's smarter than us, which can completely model our minds, we will appear to be nothing more than fancy robots. Automatons.
Think about the things we say are "deterministic" or "don't have a choice". We say this because we know what the inputs and outputs will be. When you push a button, you know a computer is going to do a certain thing, consistently. Or... well, sometimes when you push a button, the computer crashes. Sometimes it crashes for no readily apparent reason at all, without you doing anything, and you get angry at Microsoft. But you do this because you assume someone, somewhere, made it so there's a reason this computer should crash, and that someone is an idiot because they just caused you to lose your spreadsheet. So since you think there's an understandable reason for everything a computer does, it doesn't have free will.
The systems we attribute choice to are the ones where the inputs and outputs are beyond our understanding. It used to be that a lot of the inputs and outputs to nature, and how they were processed, were very confusing to us. We didn't even have enough information to attempt to model them. So we said that God brought the seasons, and God made the sun come up and go down, and God, with His free will, decided who would live and who would die, who would get the black plague or be destroyed by earthquakes or volcanoes.
Now we're starting to understand a lot more about these systems, and build systems we know are deterministic in how they operate, but they seem to magically do things and we don't understand how. So it becomes a lot more plausible that the natural world has no "free will". That there are no free moral agents intervening in nature on our behalf. That there is no God, or that God is a deist God who doesn't fool around down here. But us? We're still free. Ask me why someone did something, and I can't give you a complete answer, but that's not a big deal because I can make assumptions and they are reasonably accurate. Except... those assumptions are never enough, people keep doing things that are so friggin' unexpected, that don't fit within my simplified model of how people think. Every time we try to explain human thinking in a deterministic manner, we fail, so there must be free will involved. Right? Right?
I think expecting us to be able to model ourselves, to fully understand the inputs and outputs to our own mind, is a logical impossibility. A model is a simplification. We can hold in our head a picture or an explanation of why we do what we do, but in order to encompass ALL of the inputs and outputs in our model, in order to fully explain ourselves, we would have to have a brain that holds everything in our brain and then some, which can't happen.
Since our model of ourselves (the one in our own head, anyway) will always be incomplete, it will always appear (to us) that we have a certain degree of freedom. But there will come a point where our model of ourselves in a book is close enough to complete that it will be most plausible to say we don't have free will. Because we'll be able to say "Ok, these were the starting circumstances, and this was the end result. Was that what our model expected?" And we look it up in a book, and the answer is always yes. Or we get two or more psychologists together, who together have the mental capacity to encompass the full model, and they can give us an answer as to why we did what we did, because together they have all of the pieces. Or a computer model, without our limitations of memory and processing speed, gives us consistent answers. This is the slightly scary one to me, because whoever owns that model will be able to make people do whatever they want, within the limitations of the things they can control, and the people will not have the capacity to understand how it's done. And away goes the idea of free will. The corporation that owns that model will know how to make you buy whatever it wants you to buy (or will know it can't make you buy it, at which point it will not bother trying to sell it to you). We're already seeing marketing approaches that have more knowledge of human psychology than most humans do, that know which "buttons" to "push" to make people buy despite their intentions not to... and those models will only get better. Our decisions will become less and less a matter of our free choices, and more and more a matter of influences deliberately imposed upon us by people (or computer models under the control of people) who understand how we work.
Does anyone have a reason why this can't happen, other than that you believe by faith in a book that says it can't? In other words, can you point out a flaw in my reasoning about why we think some things have free will and others don't, and why we think we have free will at this time, and the direction in which this debate is heading?