1. A communication management system, comprising: a first rule database which stores a rule for extracting specific communication data among communication data; a search unit which acquires communication data and searches the first rule database to check if the communication data complies with a rule stored in the first rule database; an output unit which, when there is detected communication data complying with a rule stored in the first rule database, outputs the communication data; an update unit which accepts a change in a rule for extracting specific communication data to analyze a communication data with reference to other communication data when the communication data against which a warning has been issued by reason that the communication data does not match the rule stored in the first rule database is analyzed; a second rule database which stores an updated rule changed by the update unit; and a database server which transmits the updated rule changed by the update unit from the second rule database to the first rule database, and reflects in real time, the change in a rule.