Someone on the defensive is concerned with justifying their actions or words. They have a defensive attitude as they try to protect themselves.
If you know that to defend is to protect, you have an idea what defensive means. When a person is acting defensive, they're trying to protect or justify themselves. People who are insecure or guilty tend to act defensive. Also, defensive players in football try to prevent the other side from scoring, just like defensive military strategies try to protect something. When someone has a defensive attitude, or is forced to defend something, we also say they're "on the defensive."