I consider myself quite the determinist(incompatibilist, hard determinism).
For me, it all comes down to one thing.
Can your brain(a physical thing), violate causality. If it cannot, then that means that given sufficient information on the variables(causes) that process in your mind to create a "choice"(effect), could be calculated beforehand, rendering free will an illusion.
That would be so, if (A) your brain and the world around you was actually deterministic, and (B) if you actually had enough information to always do the best choice, instead of taking a guess between 2-3 choices that look good enough.
The reason the world is not really deterministic is: quantum mechanics and brownian motion.
E.g., you constantly get C14 from the air, and you don't really know in which mollecule in you they'll end up. Maybe it will be in a sperm cell, maybe in your brain, maybe who knows where else. You get about 2000 DNA breaks per year due to just C14 decay. Some are repaired right, some aren't.
I'll give you a dramatic example of where a random mutation arguably changed history: Queen Victoria. Nobody before her in her family had Haemophilia, but she obviously had that gene broken in one of her two chromosome sets. And gave it by royal marriage to half the royal families of Europe.
Arguably: the Russian heir's bad case of haemophilia (made worse by idiot doctors treating it with aspirin, ffs) caused the resulting influence Rasputin gain of power and influence at the court. (Rasputin's prayers only "helped" in as much as he chased the doctors away when he was on the case, so no more aspirin for the prince, so the horrible suffering ended. But it sure looked like Rasputin could work miracles as a result.) And both combined arguably filled the glass and caused the communist revolution.
One gene randomly broken in a sperm cell => half of Europe plunged in totalitarianism, and tens to hundreds of thousands killed by Stalin. That's the kind of thing that minor things cause.
It's things that you just can't predict. Not in the sense that "you don't know enough", but as in, "nuclear decay is truly and fundamentaly random and non-deterministic."
Even in a guy's brain, take things like alcoholism. Some synapses get hyper-sensitive enough to fire randomly and cause seeing pink flying elephants, others not so much. Again it's things you can't really predict because they rely on one mollecule being here instead of there.
Etc.
So basically even if you could actually know _everything_ at a given moment, down to the state of every single atom and electron, the world is fundamentally unpredictable from there. You _can't_ look at that and say what will happen in 1000 years.