Yes, it is justified for the inhabitants of Kosovo to demand independence, because the people of Kosovo have suffered greatly at the hands of their government, and would live more free in their own state. Most modern superpowers already recognize Kosovo as its own state, and mediation provides a path for Kosovo to join the European Union. With so much support from the modern world, it is fair that Kosovo demands its independence.
No, it is not justified for the inhabitants of Kosovo to demand independence, because that would create spirals into civil war. There has been conflict in that region on and off for many years. It is more important to have peace right now than to be fighting the inevitable conflicts of another indepenence initiative.