Your Argentina example relies on people whereas the 2-way peg for sidechains should be handled completely automatically by the protocol (although for the interim solution using a federated peg that is not the case). So you don't need a centralized authority to make the commitment.
You might check these papers out for more details on sidechains and pegs:
https://blockstream.com/sidechains.pdfhttp://www.rsk.co/blog/sidechains-drivechains-and-rsk-2-way-peg-designYou can create a sidechain for bitcoin, but doing it for ETH for example, would be a "transfer" between bitcoin and an alt-coin, not a sidechain. ETH has its own rules for creation of ETH whereas a prototypical sidechain would have coins created and destroyed when there are "transfers" to and from the sidechain. This means, for example, you wouldn't have different inflation rules for the sidechain. The papers above (and many others) have much more detail.
When the government of Argentina says they're going to peg the peso to the US dollar that means that if you come and give them a peso they will give you a US dollar in return. That's a 1 way peg.
A 2 way peg would mean you could get a peso for a dollar in the US and you could get a dollar for a peso in Argentina.
With cryptocurrencies a peg can't function this way since there isn't any authority, such as a national government, who can make such a commitment.
So what are we talking about when we say 2 way peg?
According to my understanding it means that if you send an amount of BTC, let's say amount X to a particular address A, this address is associated with a different cryptocurrency, ETH for instance ,on blockchain B.
Then having sent X of BTC to A you will have some amount of ETH proportional to X on blockchain B, until you decide to reverse the peg and have your BTC insead of ETH. Is that how it works?