Why is Milei begging for a bailout?

There are two primary reasons.

First, he pegged Argentina’s real exchange rate too high, hoping this would appease voters by getting inflation down more quickly.  That was a miscalculation.  It also was a violation of market or libertarian principles.  The problems here are not an instance of market failure, rather Milei forgot his own principles.

Second, the opposition did very well in a recent election.  So everyone is afraid the reign of Milei, or like-minded leaders, is not going to last for so long.  That precipitated a crisis in the markets.  But that is hardly an argument against Milei, even though it happened on his watch.  It is an argument against the likely alternatives to Milei.

So it is a mistake to read recent events as somehow a repudiation of market or libertarian principles.