Why?   Because being Close Minded is perceived to be a bad thing.   

In my definition of Open Minded there are two significant terms:
   → unconvinced
   → new information

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

If one is unconvinced of the Truth, one is lost.   

If one is unconvinced of a false-hood, one is protected from the consequences of deception.   

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

New information is not necessarily good information.   It may, in fact, be bad information and lead to the person being deceived.   

The injection of new information has the tendency to convince an Open Minded individual.   

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

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