The Calvinist / Arminian debate is often seen from the perspective of “free will”. I am not sure this is really the best way to characterize the true nature of the debate, to ask the question whether man has a free will or not. Better to ask what “will” is, how it functions, and where it comes from? What is it that determines the choices we make?
Most Reformers are comfortable using the term “free will”, in fact. We have to define it properly, of course. I don’t think it’s best to discuss predestination at the point of man’s decisions frankly, because man is truly called to make a choice constantly in Scripture. Predestination rightly understood takes place a step back from the will, at the point of man’s nature from which will arises. So man’s will is free in the sense that he is not compelled from any outside source from ultimately choosing to follow God or not to follow God. The will then is free to be what it is- the faculty by which, when confronted with choices in my life to make, I prioritize those choices based on my values and my understanding of how those values will be best served by those choices, and then take action based on my perception of what will best serve my values. People do this all the time, and do it well. The emphasis in predestination is therefore properly on the nature, and how the nature of man can become something capable of choosing good, or even desiring to choose good. This is the problem- our natures are corrupt, desiring bad things, and our will reflects this. It’s not that the will is malfunctioning, or restricted in some way. Our will is properly reflecting our values. A bad tree cannot bring forth good fruit.
This helps us address the fact that God constantly calls on man to choose to obey God. Ezekiel 33:11, for example- “Turn, turn from your evil ways! Why would you die, O Israel?” This should not be a challenge for the Calvinist, because as the rest of Ezekiel makes clear, the unbeliever cannot, will not turn from his ways until the stony heart is taken out of his flesh and he is given a heart of flesh (Ezekiel 36:25). Only then will he hear the word of God and do it. Once the nature is changed, the will follows.
As the quotes above show, the Scriptures talk frequently about the choices we make and where those choices come from. Choices we make simply are not made in a vacuum. They come from our nature, which is completely corrupt in Adam. We hate God, hate his image in others, and our choices reflect this. This is why regeneration is necessary, why a transformation of the nature is necessary. “You must be born again”, as the Scriptures tell us. Only with the transformation of the nature can different choices begin to happen.