Reading through the comments of that post, I understood this to be the gist of the argument for why you would give up the $100:

Before knowing the outcome of the coin flip, you would have taken the wager to pay $100 for a 50% chance to win $10000. Alternatively, if Omega had asked you to "precommit" $100 in case you lost, you would still agree -- its nearly exactly the same thing. (Technically it's an even better wager.) What if Omega asks you to precommit a witless future self? You would like to pre-commit your future self.

So you, your current self, while trying to decide whether to pay Omega or not, have decided that you would actually like to precommit a future self to paying the $100. How do you do that? By being that future person in the present and committing your current self to pay the $100. Indeed you lost, but being consistent with "being a payer" is what you decided you wanted.