Turing didn't just dive right into the man vs. machine game for a reason. Without the background information provided by his choice of even mentioning the man vs. woman game, and mentioning it first, one would not have the proper information to clearly and informatively interpret what they were reading. After reading the description of the man vs. woman game, one would have something to compare the man vs. machine game description to. Without that, one would just read the man vs. machine game, and simply accept, as fact, that if you can distinguish a man from a machine in the game, than the machine must not think. After reading the man vs. woman game, one would be able to say that just because you can differentiate between a man and a machine, doesn't mean that the machine doesn't think. They will have read the man vs. woman game, and have something to compare it to.