One possible reason is that the codons were selected for more specificity/more amino acid possibilities to provide more diverse proteins doing more diverse jobs. A very small change to the genetic code can produce a wildly different protein. Another possible reason is that life has one common origin through one ancestor of all currently living things which used the genetic code which we find in all organisms today.
Work Step by Step
Use your imagination to see how descent from a common ancestor could explain this shared set of traits and how the same logic about the evolution of genes, especially after they duplicate (see earlier chapters), could be applied to the codons in the genetic code.