Leaving the nest will teach you so many things and the pros and cons of living away from home: to manage the money, to clean the house and clothes, to cook on your own... It's also interesting to share ideas with other people and to see that you're not always right, in fact, you can be always wrong from the point of view of others. Remember: travelling can cure nationalicisms.
Moreover, you improve in language skills and in your working experiences. In other country you feel like doing whatever and that's why you do all those things you'd never be able to do in your hometown. Things as simple as dancing and singing in the rain but so comforting.
To end the pros, I must say that the best argument for is that everything you live while you're 20 will stay forever in your mind so seize the days and more while travelling. Take photos. Make a list of thing you want to do before dying.
On the other hand, it is not always so awesome. Due to your young, some people will try to cheat you, you'll feel alone and, the vast majority of time, homesick. But what the hell?! What if you can't afford an expensive trip? Fill a bag with your basics and take the first plain to wherever. ADAPTATION. This is the perfect word to describe travelling alone.
Now, come back to that place: take a beer, talk to your new foreigner friends and, why not, kiss the love of your life, that person you met travelling when you were 20.

