6. Traditional arithmetic builds Christian character.
Do you believe Philippians 4:8? Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report; if there be any virtue, and if there be any praise, think on these things. Story problems do more than help children apply mathematical knowledge. They influence the thinking of the children by the way they are presented and the subject matter of the word problem. They can show people working, tithing, enjoying God's world, and engaging in Christian activities, or they can show only secular interests and behavior. The A Beka traditional arithmetic program uses word problems that help to develop strong Christian character.
7. Traditional arithmetic lays the foundation for higher mathematics.
Elementary arithmetic, quite naturally, begins with the most elementary, basic arithmetic processes. Children learn best when they proceed from the particular to the general, from the concrete to the abstract. Traditional elementary arithmetic properly emphasizes the facts of addition, subtraction, multiplication, and division that accord with the child's stage of mental development and have immediate practical application. Traditional arithmetic lays a solid foundation for high school math, which appropriately (but still gradually) introduces the child to a higher level of abstraction. He learns and understands algebra and all higher math better if he masters arithmetic first.
And there we have it. The foundation for using traditional arithmetic. This is certainly the way I learned math growing up. I see absolutely no reason to switch to a different method.