People say anyone can become a leader. Is it really possible? Aren't there people who traits make them unfit to be a leader?

Leadership is not the tea of everybody's cup. The second half of your question is correct that there are certain traits which a dynamic leader possess, certain traits a dictator possess so on and so forth. 

Leaders have different DNA and they go by their own will power.

Most people are not and never will be leaders.   This is good, because don't need many leaders.

However, EVERYBODY can improve their leadership skills.