I think that the argument is not so much that if you succeed in incorrectly convincing yourself that you have (libertarian) free will, it is not your fault. Instead, I think the argument is that success in willfully convincing yourself that you have free will (or convincing yourself of anything else, for that matter) implies that you have free will. If you didn't have free will, then you did not really willfully convince yourself of anything - instead, your belief (or lack thereof) in free will is just something that happened.
Sure, but the question is why you should try to convince yourself of libertarian free will, instead of trying to convince yourself of the opposite. If you succeed in the first case, it shows you are right, but if you succeed in the second, it shows you are wrong.