The easy problem was that many computer programs used two digit dates

There were many, harder problems. Many of the programs were old and poorly structured. They were also written in older, less popular languages, like COBOL. Many of the original programmers had retired or died. Most younger programmers used more modern languages like C. Large numbers of older, retired programmers were brought out of retirement in order to work on the code

Modifying old, poorly structured code is difficult. Many of the programs had gotten very large and convoluted over time, and many of the complex behaviors were undocumented and very much non-obvious to someone seeing the code for the first time. Attempting to modify complex code often results in serious side-effects that are hard to predict

Another problem is embedded systems. These are programs in machine tools, process controls, electric power generation and control and millions of other devices. Many of these devices had software that was difficult to modify. Even worse, the programmers were uncertain about how many devices relied on dates and how serious a date error might be

Computer scientists did not clearly know what all of the problems might be, and they needed to convince management to spend millions to fix the problem, so they presented hypothetical, worst-case scenarios. These were picked up by the popular press, where reporters misunderstood some of the subtlety and exaggerated the dangers even more

It turns out that the worst-case never happened. Old code was successfully modified and many companies used this as a justification for migrating their software to more modern languages and hardware

Source: I've been programming since 1972, and followed the story in technical detail at the time