Why the 2DS makes perfect sense
At first, I was really confused by the 2DS - just like everybody else. But the more I think about it, the more it makes perfect sense.
I believe Nintendo has realized that the handheld market for teenagers is gone and never coming back. Teenagers used to want the latest Gameboy, but now they want the latest Galaxy phone. Very few teenagers are lucky enough to get a smartphone AND a portable gaming system, and when forced to choose, they go for the smartphone almost every time.
So what does Nintendo do? Release a cheaper DS aimed directly at pre-teens and little kids. When parents look at a 3DS they worry about two things, will it break and will it ruin my kid's eyes. Well, the 2DS answers both those concerns. Nintendo also knows that if they can keep the 5-10 year old crowd, then they will be able to sell nostalgic Mario and Zelda games forever. I know I am not the only one irrationally excited for the remake of A Link to the Past.
Even better, they have them priced so low that they are very tempting, especially at the holidays. Parents are looking for cool gadgets for their kids. You know what looks like a great deal? Kindle Fires and other small, cheap tablets. Why buy your kid a 3DS, which with a game costs $200+ when you can get them a Kindle Fire that has tons of free games? Now, parents look at that low price point for the 2DS and are tempted. You can get your kid a new 2DS and a couple killer games and make it out of the store under $200. That's really competitive.
TL,DR: The 2DS is a great product that will help Nintendo tighten its grip on the 5-10 year old market, which is probably their most important demographic over the long term.