No. of Recommendations: 1
Great! I love it.
Having been in my previous life an Author (no, I don't mean it in a religious or not resurrection way) I admire your skills to communicate in a clear and extremely understandable way. Yes, music is communication too, maybe you should also write (books)?
One comment re
.... so by trying to argue to a receipient that there is no free will, they are admitting in the process that the receipient has free will.
Your argument is based on the assumption the philosopher's actions are based on rational conscious behavior.
But as you are pointing out yourself that there are subconscious processes one has not even knowledge and therefore even less free (conscious) will about, your argument ignores that exactly those non-conscious processes might force the philosopher to behave non-rational, in this case to try to convince the other one no matter how much the philosopher is convinced himself that it's futile.
This for example is what happens every day in discussions between Atheists and non-Atheists, Demokrats and Republicans etc. One side argues to the other, knowing perfectly well it's futile - at least if the motivation really would be to convince the other one. So it's not rational.
And therefore the cause must be other, irrational motivations underneath. For example by repeating aloud the arguments why God does not exist (or the other way around), why Trump is bad (or good) one might strengthen one's own wavering believe in that. Or one might proof to the others of the social group (of Atheists etc.) that one belongs to them. Etc. There are numerous subconscious motivations for behaving in ways that rationally make no sense, and because all of that happens subconscious you have no knowledge and no choice - which points to "Free will is an illusion".