Who we are determines choice. Adam made a wrong choice. There are consequences to actions. We can choose Christ or go on our own path. Only God ultimately know who we really are beyond the realms of time. Adam wasn't perfect. Adam was innocent & Adam was not praying that God helped him in everything that he did. When we are blessed by God we sometimes forget about God & we jump off the deep end.
This is one of my favorite questions to ask those who believe free will (incompatibilistic) does not exist. Adam should be at the center of any such discussion among christians. The theology of Adam is the primary reason I don't accept the idea that all choices are determined by nature.
If your premise is true, that our choices are determined by our nature, then that means Adam would have had to be created, not just innocent, not just neutral, but actually with a sin nature! That nature in turn determined his choice to sin. But this of course is foreign to what Genesis teaches. Adam was not created with a sin nature. God looked at everything He had made, including Adam, and declared it to be very good (Gen. 1:31). And yet Adam still sinned.
Now for certain Adam had a sin nature after his fall, just as we do also. For certain this nature is determinative. And yet at the same time God tells us we will never be tempted beyond our ability to resist (1Cor. 10:13). Again, a baffling revelation to the determinist.
What I would suggest is instead of starting with a philosophical axiom such as "who we are determines choice," why not go to scripture to derive your starting axioms? Many greek philosophers believed in the same axiom. Many theologians have been influenced by them. But the problem I think they've made through the ages is failing to look at these seemingly fireproof axioms in light of biblical revelation. The existence of choice and liability for those choices is undeniable. At the same time, determinism is also shown to be true in many cases.
Thus, from a pure biblical perspective, I would have to alter your premise to: Who we are determines many of our choices, perhaps even the vast majority. But it does not determine all of them.