Free will seems quite obvious intuitively. However, it also seems impossible.
If the brain is a bunch of matter and energy following the laws of physics, how can there be any free will? People are then just machines, like computers.
There is a simple way out of that: you could claim there's something else (eg. a soul) affecting the brain. However, the same fundamental problem remains regarding whatever is in control. If there are a bunch of deterministic processes involved, it's a machine. If it's not deterministic then it's randomness, not freedom. If something is manipulating the probabilities, then consider the processes involved in that. It's again the same problem.
It doesn't seem like any kind of process science knows about would resolve this. There would have to be some weird intentionality force in control, whose properties I cannot imagine. Now suppose this magic free will force does something. What caused it to do that? Again, the same sort of problem can arise.
Another way to look at it is that free will supposedly cuts the chain of causation. Events are generally consequences of other events, but free will events are supposedly caused by a being with free will and not a part of the overall chain of consequences. That doesn't even seem true; actions by people do seem to be related to causes. Yes, it's possible to stop a cause from leading to action or redirect it, but that's really only due to another cause. Oh, and choosing between causes is also due to causes. Once again there is a risk of infinite regress.
Based on all of this it seems like free will is probably an illusion. I can't say that's certain, but based on science it certainly seems far more probable than that free will exists. Yet from my own point of view, it seems so obvious free will exists, and the idea that it doesn't exist seems unacceptable. A world without free will would be like a movie, either entirely deterministic or with random elements, except that I'm watching the movie as a character in it and I constantly have a delusional perception that there is free will. I hope that's not the way reality is.