One of my most favorite observations: "Humans are not rational animals...rather, they are rationalizing animals". And hence the choice that you make, is always right. Because, your mind is always ready to rationalize your chosen option.
I once asked to one of my introvert friends: "why aren't you joining the party with others? why do you behave like that?". His answer: "I don't like parties and the loud music there...!" You can easily understand from the above example that, my friend was trying to rationalize his introversion. But, that would be only half the analysis that could be done here. Actually, he is not only rationalizing his introversion by blaming the loud music, but he is also (although in his mind) rationalizing his choice of not meeting new/unknown people at the party by thinking that, he is an introvert!
Are you an introvert? Well nothing wrong if you are one, but remember; you are an introvert because you chose to be so, and similarly and an extrovert is an extrovert because he has decided that he would behave that way.
Is there any wrong in being one or the other? No.. I am an ambivert (A personality trait including the qualities of both introversion and extroversion), so I know both of them very well. And I am an ambivert by choice! I decide, when I want to an extrovert and when not. And that makes my very flexible to be accommodating of any situation I face.
So, Is it possible for an introvert to become and extrovert with time and vice-versa? Yes! All these habits comes to us because of environmental influences. And its us, who decide the environment in which we would like to be. The problem with people is that, they think too much, and hence they find themselves in a situation where they do things that themselves din't want to do...