Why?   Because being Open Minded is perceived to be a good thing.   

In my definition of Close Minded there are two significant terms:
   → convinced
   → new information

To be convinced can be a thoroughly good thing or a thoroughly bad thing.   

If one is convinced of the Truth, everything is good.   

If one is convinced of a false-hood, everything is not so good.   

An expert is a person who has learned and been convinced of the principles that govern his discipline.   

A real expert is a precious thing.   That person is able to provide services that are consistently good.   

A professor may come across as an expert but they may not have sound principles and may have never verified the principles they profess.   

The second part of the definition is `new information`.   

New information is not necessarily good information.   It may, in fact, undermine the good conviction that one holds.   The result is that one is no longer convinced.   

The injection of new information has the tendency to open the mind of the Close Minded individual.   

If the person is convinced of a false-hood this is a good thing.   If however, they are convinced of the Truth, this is a bad thing - a very bad thing.   

When a person is lost - away from Christ - they may be convinced of their World View.   The injection of the new information of the Gospel can take such a person from a lost state into relationship with the Lord Jesus Christ.   

In terms of their faith In Christ Jesus a believer should become Close Minded.   Any new information that comes to them should be rejected out of hand.   

However, a believer should always be Open Minded to the scriptures and the leading of the Holy Spirit.   This enables them to grow in Grace and knowledge of the Lord Jesus Christ.