The difficulty is making it protective but light enough to not significantly hinder the spacecraft or person wearing it, all of which is covered in the article.

Poor design, flawed assumptions, manufacturing defects, inability to bear the gravitational and rocket launch forces, inability of the jacket to last the duration of the radiation exposure - these are some reasons that come to my mind on why a radiation-blocking vest wouldn't have worked for the journey to the moon and back (i.e. your question "Why wouldn't it?".)