I've had a bunch of conversations like this. Someone proclaims to know the future with virtual certainty, but when you challenge him to bet on his professed belief, he spurns your offer unless you give him even odds. Of course, if he really believed he was right, 100:1 would still be easy money. What's the explanation for the prevalence of this reluctance?
1. My rational irrationality story. A bet instantly raises the marginal private cost of error, which leads to a sharp increase in rationality. Faced with financial consequences, people suddenly - if temporarily - admit to themselves that they know a lot less than they like to believe - and bet accordingly.
2. The strategic explanation. Why give 100:1 odds if you can bargain for 1:1?
3. Focal points. 1:1 is focal, and the transactions costs of settling on anything else aren't worth the effort.
4. Norms. People think that only 1:1 bets are "fair," so - on principle - they refuse uneven bets that they expect to be profitable.
Explanation #1 is of course my personal favorite.
Explanation #2 may have some merit, but it's far from clear that adamantly insisting on 1:1 is a smart bargaining strategy. In most cases, holding out for 1:1 prevents the bet from happening in the first place. If you really know something with p=.99, you might not want to offer 100:1 odds, but why not offer 5:1 if it's the only way to get the other side to bet?
Explanation #3 works for small bets, but if anything people seem even more reluctant to give odds on big bets. (More evidence for rational irrationality, I say!)
Explanation #4, again, might explain some of the reluctance, but it's not clear that people really think that morality demands 1:1 odds. How many people really think that it's wrong for roulette to pay more to people who win on "lucky number 12" rather than "black"?
Overall, the evidence seems consistent with my view that people like to see themselves as brilliant oracles, but on some level realize that they are anything but. When you raise the cost of this irrational belief, people's residual rationality kicks in to protect them from the consequences of their absurd but gratifying self-image.
Too bad I can't think of a bet to resolve this question...