To answer this question, I think it would do well to recognize how, going back all the way into the Colonial Era, there had always been some sense of a Frontier which, over time, as the country expanded westward, was pushed further and further west as well. This perception would have been central to how entire generations of Americans had experienced and perceived the world around them: the idea of there being this vast, largely untapped world out west would have been a statement of fact, and one of those fundamental truths that defined the United States as they knew it. By the end of the nineteenth century, however, when the frontier had been settled, this would have represented a profound change, existentially speaking, and a profound break with a collective shared experience, reaching all the way back to the time of the Thirteen Colonies stretching forwards.

I am curious to know if you really mean to say "is" or if you mean to say "was."  It is hard to argue that an event that supposedly happened 120 years ago would disturb us today.

If you mean to ask why the "passing of the frontier" could have disturbed people nearer to the time that it happened, it is because the frontier was seen as the source of many of the values and attitudes that made America great.  It was the source of Americans' rugged individualism and their inventiveness.  It was the source of their egalitarianism and love for democracy.  It was the source of their optimism.  If the frontier was "closing" then those traits were in danger.  This would be a source of distress to people as it was happening.

As for the present, the passing of the frontier can only disturb us if we feel that the attributes mentioned above have truly disappeared and if we argue that their disappearence is due to the closing of the frontier all those years ago.