I'll answer that question. 2 on 1 off, 3 on 1 off is simply the schedule I keep and the athletes I train at Brand X keep. A brief history might keep things from getting overly complicated.
I am a CrossFit Trainer, I'm proud of that. As such I have been heavily influenced by Coach Glassman. In his article,
Fundamentals, Virtuosity, and Mastery
An Open Letter to CrossFit Trainers
CrossFit Journal August 2005
Coach states the following:
There is plenty of time within an hour session to warm up, practice a basic movement or skill or pursue a new PR or max lift, discuss and critique the athletes’ efforts, and then pound out a tight little couplet or triplet utilizing these skills or just play. Play is important. Tire flipping, basketball, relay races, tag, Hooverball, and the like are essential to good programming, but they are seasoning—like salt, pepper, and oregano. They are not main courses.
skill work and play
We follow Coaches lead in virtuosity in movement at BX. You will hardly ever hear a trainer telling someone to go faster. They almost always will be helping the clients/athletes to move better. In the same way we followed coaches template outlined above.
While visiting last summer three CrossFitter, Patrick Massey, Anita Tyler, and Patrick Hoffman noticed the way were training was a little different than some of the other affiliates they had visited and began hounding me to write down what we were doing and pass it on to them. Their incessant badgering eventually won out and CFSB is the product.
Why do we only press one day? Simple, most of us were "understrong" in the squat/deadlift department but already pressed at bodyweight.