I think that there is a complex answer, or several complex answers, to this question. Initially, I would say that all study of history is relevant and meaningful. I fully admit that I am biased as a History teacher. I find that all studies of history as being relevant as they tell or reveal aspects of national heritage or narratives that help to explain the past and how it fits into a sense of a nation's identity. I don't think that there is anything wrong in saying that someone from a country should be fluent or proficient in that nation's history. It is important to study one's own history in order to understand national identity, sacrifices that have been made, and yes, mistakes that have been committed in one's own history.
Having said this, I think that one has to be very careful in placing one history over another. I think that the idea that President Obama said a while back is relevant regarding exceptionalism when he said that each nation believes in their own "exceptionalism." I think that studying as many histories as possible lends credibility to people becoming global citizens and understanding more about different cultures. I think that it is important to validate these voices and not silence others. Recently, in India, a member of a national political party stirred controversy when he commented that certain "Indian" texts should be taught over other texts and implied that there is an "Indian" identity and should be valued over others. In a globalized world, ideas and notions are exchanged so freely that it is important to value as many heritages as possible, draw out commonalities, and even point out where mistakes and errors have been made. It is in this light where I think that it is important to study your own history as well as that of others in the modern setting.
I think you need to study your own country, but be aware of others as well. We tend to view things in America by our own slant, in our own best interest. Everything does not revolve around us. It's important to know the truth about events America was involved in.
The history textbooks of the United States present world history in which the U.S. was involved as the "world according to America." Reading a history book from Germany, for instance, about World War II gives the reader an entirely different perspective. Watching the news broadcast from American stations is often different that watching the news on the BBC. So, it is indeed important to attain knowledge from many sources.
As I think back, there really wasn't much taught to me in public school in the US about world history. That may have changed a lot since I graduated, but it strikes me as odd that more wasn't taught about life outside America.
Very well said, akannan! Having one country's perspective only will hinder you from relating to others from around the world. This would be the case for religions as well. The more well rounded you can be in this regard, the more compassion that can grow, too.