Because it's not sustainable. Economists of different stripes all tend to agree that the peso is overvalued, and this starts producing all sorts of different macroeconomic distortions as we're beginning to see.What’s stopping him leaving things exactly as they are? In spite of the insane prices most Argentinians aren’t complaining (beats me why) about the situation, so he has no reason to do much of anything
Look at the above referenced Big Mac Index for one small example. Since June, the price of a Big Mac sandwich has risen to $8,000 making the peso 38.1371% overvalued compared to the dollar, and it's going to continue to get worse month after month.
While this example may seem only applicable to a single hamburger, it can be extrapolated broadly. Brazil has devalued the Real, and it exports basically the same things we do, to the same countries, and in much higher volume. If you need to buy soy and Argentina offers the same soy as Brazil for a 38% premium, why would you buy it? This is where the big problems start, because it means less dollars for the BCRA, and less dollars to intervene in the forex market with to keep the peso artificially valued, and to service international debt.
It flew under the radar on the week of Milei's anniversary, but the BCRA still operates in basically flat or negative net reserves when assets and liabilities are accounted for, and this means that Argentina will require an IMF or private loan disbursement to be able to make payments on the soon maturing international debt in H1 2025. The pro-Milei press likes to say stuff like "Incredible! Look how many dollars the BCRA bought in [month]!" but the BCRA did so because that's how they pay these loans. If you have a savings and checking account it would be akin to your spouse saying "Wow! My wife just put another $1,000 in our checking account this month!" despite the fact she did so because the mortgage payment is scheduled to be withdrawn the following day. Seems a lot less incredible, doesn't it?
Anyways, while monthly inflation is now a single digit, people are only spending money on the basics (rent, food, utilities, etc.) and this continues the economic recession, job losses, shrinking tax base, etc. which put further strain on a country to remain in a budget surplus/able to service it's debts when it's international reserves are flat, and it's currency is overvalued. Austerity is often penny wise and pound foolish because it can end up costing societies millions more than they end up saving by diminishing a country's capacity to grow and collect tax revenue.
Milei knows that the status quo isn't sustainable, but he's also afraid of letting the market determine the exchange rate because everyone knows it will cause upwards of 40% to do so. This is where the title comes from: a horrible mistake. He had a chance to let the market determine the exchange rate, to let the chaos occur during his first year, to keep the devaluation in line with inflation, but he chose not to in order to kill inflation faster, and now he will reap what he has sowed.