The strongest argument against free will does not depend on determinism being true. It works either way, which is what makes it so difficult to escape.
The dilemma
Consider any decision you make. Either it was determined by prior causes or it was not.
If it was determined, then given the past and the laws, you could not have chosen otherwise, and the real source of the choice lies in conditions you did not create.
If it was not determined, then something in the process was a matter of chance. But an act that happens partly at random is not thereby under your control. If rewinding the universe and replaying it could yield a different choice with no difference in you, your reasons, or your character, the difference came from nothing you own.
Galen Strawson pressed the same point from another direction. To be truly responsible for what you do, you must be responsible for how you are, mentally speaking. To be responsible for how you are, you must have chosen to be that way. But any such choice would have been made by an earlier version of you, whose nature you also did not choose, and the regress never terminates. There is no first link you could have authored.
The libertarian reply
Libertarians accept that determinism would be fatal, and argue that human agency is genuinely undetermined in a way that is not merely random.
The most developed version appeals to agent causation: the idea that a person, as a substance rather than an event, can be the starting point of a causal chain. On this view the agent is not simply the arena where prior causes meet but an originator, a place where something new begins.
Robert Kane offers a naturalistic version. He points to moments of genuine inner conflict, where two courses of action both attract and the outcome is not settled. If the indeterminacy sits precisely there, then whichever way it resolves, the agent wanted it, has endorsed it, and can fairly be said to have made it their own.
Why critics remain unconvinced
The standard objection is that these accounts name the problem rather than solve it. Agent causation asserts that persons can originate chains without explaining how a physical being does so, or where in the brain such origination would sit. And Kane's conflicted-will account still has the resolution turning on an undetermined event; calling both outcomes wanted does not obviously make either one authored.
So the dilemma stands. If it cannot be escaped, one route remains: deny that free will ever required escaping it.