Look into Kurt Gödel's incompleteness theorem, and the philosophical implications of that.
A lot of times, when we're dealing with the assertion that we don't have free will, we're analyzing that according to rule-based systems. The system that we use to evaluate truth isn't entirely rule-based, and is necessarily a superset of what we can consciously evaluate.
In effect, some less-complex system that is a subset of your larger mind is saying 'you have limits, and they are this.' But your larger mind disagrees, because that more rule-based subset of rights is incapable of knowing the limits of its superset. Though, we just feel like it's 'off'.
If it feels like it's off, there's a good chance that the overall way you're thinking of it isn't right, even if the literal thing you're focused on has some degree of truth.
In short, it's possible to know something that is technically true, but that isn't interpreted correctly internally.
If you accept the model that you have no free will without processing the larger feelings it evokes, then whether or not your internal sense of free will is rule-based, you'll artificially limit the way you think to filter out the internal process you think of as free will. ..and that can have massive consequences for your happiness and viability as an organism, because you've swapped away that which you actually are for labels and concepts of what you are - but your concept is fundamentally less complex and led capable than you are as a whole.
Fortunately, rule-based systems break when faced with reality. It's just that it can be very painful to go through that process with what you identify with.