Why might it be important for EU countries to share borders?

Answer: for trading purposes.

Explanation: it is important for European Union countries to share borders for trading purposes. Since the European Union, countries aim free movement of goods, services and even human capital, having open borders adds to the ease of trading. Similarly, European Union countries offer privileges to the employees providing them the ease of movement between European Union countries offering them jobs. Moreover, the open border facility also reduces disagreements between those countries.