Has anyone in history ever successfully convinced a 20 year old man to do the reasonable and sensible thing?
There are some good suggestions here, though if your brother has the hardheaded outlook you've described, it's tough to imagine him sitting down to read books on safe riding. If he won't go to a class where he actually gets to ride a bike, I'm not sure that reading a book about riding a bike would be the carrot he needs. Offering to take the course with him is a good idea too.
But, you may find yourself having to make a tough decision here. If he really is that bad on a bike, and he won't take any of the suggestions offered here, and you unequivocally feel that he's a danger to himself (or to me and the rest of the public) when he's on a bike, you can resort to the nuclear option if it's available in your state.
Many states have a law on the books that can require a licensed driver to be forced to take a reexamination if a credible report is made by law enforcement, medical personnel, or a member of the public that the motor vehicle operator is an unsafe driver. It's the sort of thing that happens when an elderly driver becomes unsafe, and a family member reports them to the DMV; the DMV requires the elderly driver to take another exam, even though they already have a license. If they fail, their license is revoked.
If you truly feel that his skill level (or lack of it) makes him a danger, then tell him that unless he agrees to take the MSF course and let an unbiased instructor judge his skill level, you'll notify the DMV that he doesn't possess the necessary skill to be operating a motorcycle. They may take no action, or they may order him to take another motorcycle exam. The DMV instructors know from the paperwork that the driver is there for a skills reassessment, so they're likely to scrutinize the driver a lot more closely. It could result in your brother having his motorcycle license revoked.
This is definitely the hardest assed of options. But, if your brother ignores all your efforts, and you absolutely are convinced he shouldn't be riding without additional training, you could use this as a last resort. Only you know how truly unskilled he is; is he bad enough that you're willing to go this route? Because if he isn't, then maybe your best option is to just leave it alone if he won't follow your advice.
"No matter where you go, there you are."