Lex specialis in deciding between the intuitions of freedom and causality

In the book The Science of Freedom, Rav argues that when there is a conflict between the intuition of causality (which leads to determinism) and the intuition of freedom (which leads to libertarianism), we should use the doctrine of lex specialis and therefore prefer freedom over causality.
And I don't understand, because determinism also claims to explain our intuition in a deterministic way (as the Rabbi himself mentions in the book). So according to the determinism method, the intuition of freedom really exists, but despite this, it is impossible to prove from it the existence of freedom of will. So determinism does not contradict any intuition, but rather it simply claims that although the intuition exists, nothing can be deduced from it. So why should it prefer it and thus no intuition will be rejected (but only the conclusion that we can deduce from it)?