Thanks for the important question. I will offer some suggestions as to why this war remains relevant thirty years later.
From a purely military standpoint, the Falklands War could not be more relevant today for classroom study. Fighting for the Falklands was quite an extraordinary undertaking for the British given the vast distances and their lack of wherewithal in this very remote region of the world. Everything they needed they had to take with them over 8,000 miles, in what is often called expeditionary warfare. Contrast that to what has been happening in the Middle East for the last 25 years where thousands and thousands of troops from multiple nations have rotated in and out of an established military theater, in most cases not even bringing their own equipment because equipment was waiting for them in theater, along with deep draft ports, airfields and roads. None of that existed in the Falklands, not a single road outside of Stanley. Today western militaries are refocusing training on expeditionary-type warfare into austere environments. Units were very much trained for quick deployments back in the 1980s. That is no longer true. Although they have performed remarkably well in recent years, men and women in the military no longer are skilled in deploying quickly with their own equipment and supplies to places with little or no useful infrastructure. Countries like the US and UK have recognized this and have refocused training. The Falklands War has provided them a good vantage point for reflection. There is much there to refresh memories and provide thoughts for planning.
There have been many fine books written about the Falklands War. Mine is the first to tell both the history and the impressive logistics that enabled the British victory. I have dedicated it to the thousands of British men and women who worked so magnificently behind the scenes to support the war effort from the UK all the way to the Falklands. They in particular deserve an account of their remarkable achievements. What the British achieved so quickly and so far away remains quite unique in all of military history. Much of it happened behind the scenes. It is quite a story.
Finally I would suggest that understanding why nations choose to fight and how they win or lose will always remain relevant. In 1982 few anywhere in the world knew of the Falklands, and yet in less than three months nearly a thousand men died over those islands. Today, some saber rattling continues. Reflecting back on what happened thirty years ago might soften some of that rattling. If it does not, then reflection certainly will reinforce some of the challenges that await.