Why "Mon père est dans le prison." incorrect?

The correct expression is "mon père est en prison" because it means 'incarcerated' which is a general statement as explained in the lesson above.

Note the absence of the article (by the way prison is feminine so it would have been la prison).

Just to comment further. If you say "mon père est dans le prison. " It doesn't mean he is incarcerated but more like he is in the building.

-- Chris (not a native speaker)

very good point!
Something like " mon père travaille dans la prison de Fresnes."

CORRECT

IT SHOULD SAY "MON PERE EST EN PRISON."

I have exactly the same question.  An example later on uses dans la when saying "there is a riot in the prison"  My firstt inclination is that they are using prison in the dans only sentence to indicate prison as place in general, but what if there is only one prison he could be in?