Being accused of habitual denial implies that I have the freedom to exercise such denial.
Yes, and presumably you decided on pointless unargued denial and assertion for some reason. Perhaps because you thought one more assertion might change somebody's mind, or you couldn't be bothered to engage in the actual arguments, or...
The point is that you arrived at that choice because of who you are (the result of nature, nurture, and experience) applied to this online conversation. You couldn't have decided to not be yourself, or to think like somebody else. You can't be free from being yourself, it wouldn't even make sense.
That's why your freedom is compatible with determinism. In that case there is a "something" that can do as it wants and has the ability to choose.
If you insist that a choice can't be fully determined by pre-existing reasons (both internal to the chooser and external) there is nothing left to make a choice - the chooser has disappeared entirely. If you then insist on no randomness a choice will never get made.
What you are saying doesn't accord with our experiences of making choices, is contradictory, and logically impossible.