When are you saying the choice is determined?
What is making the choice?
How does the system accommodate novelty and uniqueness of situations?
Your brain (or mind, if you want to keep the idea of a soul open, for the sake of argument) is a sophisticated information gathering, processing, and evaluating system that has evolved (been magically created) to deal with abstract concepts, have hopes, fears, likes, dislikes, and all the other stuff that makes us the people we are, and which has the ability to make choices based on all those things.
None of that changes the fact of the logical necessity that down at the "nuts and bolts" level, things have to happen due to causes or not - and if not then they must be random.
You're trying to deal with separate levels of abstraction and it really doesn't work very well. You can sort of see it because you have a particular personality and way of thinking and we can see that that is because of some combination of nature and nurture. So it's sort of possible to see that we make choices for reasons but you can't hope to unravel all the layers.
To use a different example: if you want to understand why a moth flies towards a flame, you wouldn't be talking about the deterministic interactions of the atoms it's made of (even though that is the 'reason'), you'd be talking about the evolution of its behaviour with respect to light sources and so on.