Bets like the one discussed here are a rhetorical tic of the "rationalist" community.
> ...parent's argument sounds reasonable to me.
Kinda sorta. It's just a weird ritual of theirs to demonstrate commitment, and they often have a really hard time understanding that their weird rituals and mores are not universal and they can't reasonably go around expecting random people on the internet to follow them. Challenging someone to a bet like this comes off exactly as a challenge to prove your commitment by putting a bucket on your head and banging it with a stick for an hour, just because that's some weird thing the challenger's friends do among themselves.
I agree that in practice, it's pretty likely that the author of the piece refuses to bet at least in part because betting substantial sums of money on outcomes that are non-central subjects of wagers (i.e. not an explicit game of chance, sports, politics, etc) is socially unusual. But I also think that if he was very confident he'd be happy to take the money.
The bucket on head example certainly is weird. I just don't see how that's related. The logic I'm seeing is 1) the "rationalist" community does x, 2) I don't like the rationalist community, 3) so x is stupid. Is there more to it?