During transcription both the strands of DNA are not copied because
(a) One segment of the DNA would be coding for two different proteins
(b) It would complicate the genetic information transfer machinery
(c) It would prevent RNA from being translated into protein

First, if both strands act as a template, they would code for RNA molecule with different sequence, and in turn, if they code for proteins, the sequence of amino acids in the proteins would be different. Hence, one segment of the DNA would be coding for two different proteins, and this would complicate the genetic information transfer machinery. 
Second, the two RNA molecules if produced simultaneously would be complementary to each other, hence would form a double stranded RNA. This would prevent RNA from being translated into protein and the exercise of transcription would become a futile one.