I find the 'Bayesians' offering bets to be a very annoying phenomenon for mostly this reason. Let's say I want to convince you that I know something. I can start offering bets on it, trading future money for today persuasion (which is also a resource that can then be used to make more money elsewhere and come up ahead even if the bets were losing. This persuasion can in some cases even be used to try to win the bet after all).

edit: also, with regards to "you offered the bet because you know the coin came up heads, so I won't take it", I can anticipate this and "offer" you a losing bet, knowing that the offer will make you update and the bet won't take a place (or is unlikely).

'Con' in con artists stands for confidence, and acting confidently (offering apparent bets, i.e. bluffing) is a big part of it.