If a DNA letter is one of A,T,C and G, and there are 3 billion base pairs, why don't we say that there are 6 billion letters in the genome?
If a DNA letter is one of A,T,C and G, and there are 3 billion base
  pairs, why don't we say that there are 6 billion letters in the genome?


It is a convention, and stating the actual number of bases would not add any information, but would actually lead to more confusion. It's like saying 


  I have six pairs of socks


vs.


  I have twelve socks.


It means bascially the same, but now one could assume that these twelve socks are not from actual pairs (e.g. twelve left socks). The same goes for DNA. Saying we have pairs of bases emphasizes the redundancy of the DNA double strand.