Why should you care about what happens in other countries?

There are two good reasons to care about what happens in other countries. In purely practical terms, other countries do have an effect on your country. Every country has some degree (and often quite a lot) of commerce with other countries; you export products to them and import other products from them. The US, for example, imports a lot of oil. So, what happens in other countries has economic consequences in your country. There are also immigrants, both legal and illegal, who have an effect on your country. Or, you too may decide someday that you would like to live in another country. And when things go particularly badly, sometimes another country will go to war with your country, which also has serious consequences. Even if a country does not declare war, it may support terrorism. Other countries can be dangerous.

The second reason to care is simply that human beings live in every country, and since we are all human beings, we should care about each other. This is an important part of what it means to be human. If you do not care about other human beings then I would consider you to be overly selfish (not that you necessarily care what I think about you).