I recently attended the Parents' Course at IAHP and the reason they gave was that of the two, reading is the more important skill.  So, when a parent is just starting to implement any sort of program with their child(ren), they recommend that they start with reading and be sure that program is going well before adding another program. However, for a parent who is already in the swing of things and their program(s) are going well, both can be done simultaneously - in fact, several programs can be done simultaneously.
HTH!

Kathy