This corresponds with what people actually do. For example, when Stephen Diamond said on Overcoming Bias that there was a 99% chance that Clinton would win, I said, ok, I'll pay you $10 if Clinton wins and you can pay me $1,000 if Trump wins. He said no, that's just a break even point, so there's no motive to take the bet. I said fine, $10 - $500. He refused again. And obviously that was precisely because he realized those odds were absurd. So he in fact updated. But insisting, "you have to admit that you updated," is just a status game. If you just offer the bet, and they refuse, that is enough. They will update. You don't have to get them to admit it.
I don't think not believing in one's probability is the only reason to avoid betting. There's also a lot of physical resistance for many people.
Even if he believed in the odds it would be very irrational to take your bet. He would get better odds on PredictIt and PredictIt is likely a more trustworthy third-party to pay him in case he wins the bet.
(Warning: completely obvious reasoning that I'm only posting because I haven't seen it spelled out anywhere.)
Some people say, expanding on an idea of de Finetti, that Bayesian rational agents should offer two-sided bets based on their beliefs. For example, if you think a coin is fair, you should be willing to offer anyone a 50/50 bet on heads (or tails) for a penny. Jack called it the "will-to-wager assumption" here and I don't know a better name.
In its simplest form the assumption is false, even for perfectly rational agents in a perfectly simple world. For example, I can give you my favorite fair coin so you can flip it and take a peek at the result. Then, even though I still believe the coin is fair, I'd be a fool to offer both sides of the wager to you, because you'd just take whichever side benefits you (since you've seen the result and I haven't). That objection is not just academic: using your sincere beliefs to bet money against better informed people is a bad idea in real world markets as well.
Then the question arises, how can we fix the assumption so it still says something sensible about rationality? I think the right fix should go something like this. If you flip a coin and peek at the result, then offer me a bet at 90:10 odds that the coin came up heads, I must either accept the bet or update toward believing that the coin indeed came up heads, with at least these odds. I don't get to keep my 50:50 beliefs about the coin and refuse the bet at the same time. More generally, a Bayesian rational agent offered a bet (by another agent who might have more information) must either accept the bet or update their beliefs so the bet becomes unprofitable. The old obligation about offering two-sided bets on all your beliefs is obsolete, use this one from now on. It should also come in handy in living room Bayesian scuffles, throwing some money on the table and saying "bet or update!" has a nice ring to it.
What do you think?