It's not that the preceding brain activity and subsequent feeling of action/decision are separate; they are indeed part and parcel of the same mechanism. "Well then, because we are not aware of that preceding activity, we don't have free will." You fool, that activity is exactly encompassed inside "free will", as part of the mind-body-universe coupling (see On the Origin of Objects by Brian Cantwell Smith). Or part and parcel of the Unified Whole, the God/Buddha-Nature system we are all part of. Your rationale against it is itself situated within this free system. Don't look to the underlying mechanism for proof for or against free will, so long as you don't fully understand what's going on under the hood.*
* As a simple (though not perfect) example of how we might not understand what's going on under the hood, suppose an astronaut is sitting in a rocket, about to launch. The astronaut is our free will, the rocket is our hand/body. The astronaut pushes the button to turn on the engines, and the rocket surges upward! (Or, if you wish to nitpick, replace "astronaut" with "engineer in control room", the analogy is the same.) "But," an outsider interjects, "We could actually measure that several seconds prior to the astronaut pushing the button, there was some water being ejected on the pad to absorb the blast! Since it happened before the button push, we therefore can't say the astronaut caused the rocket launch, thus there is no astronaut!!" *Picard facepalm* That person just doesn't know that the astronaut-rocket-launchpad-control center is part of one big system and that, indeed, the astronaut pushing the button is a crucial component of this entire process.
Rather, look to the behavioural outcomes. If you stand at an intersection and don't know where to go, don't you ultimately pick a side, or do you stand there until you starve to death? You're not Buridan's Ass (the animal), are you? And you don't have some dice rolling homunculus ("little man") in your head, do you? If you did, who is telling the homunculus to roll the dice? That is also an intentional act. You can't dispel the need for a chooser. And indeed giving the example St. John provided, when you get sick, don't you go seek medicine? Your outcome is not preordained. You can seek for help, or not. And some people don't, like my poor late uncle, or only when it's too late.
But to go back to Libet. Even though we can measure some preceding brain activity, we still nevertheless choose, and if one has any qualms about it, the onus is on them to reconcile it within themselves, not to deny their very own experience and, worse, impose that view on others! That is just extreme scientific materialism-as-religion, no better than any other extreme religious zealotry.
Then, who is choosing? How far up the astronaut-rocket-launchpad-control center system do we have to go before we find the "chooser"? Ah, that is the question, isn't it? It can only be resolved by closely paying attention to one's thoughts, actions, and experiences in every moment, whether walking or standing, sitting or lying down. No amount of thinking about it, no amount of conceptualizing, will ever help, and will indeed simply muddy the waters more and more.
