Pokémon X does not have a mode for the left-handers among us and I'm willing to bet that there's no option for my long-suffering people in Pokémon Y, either.
The basic problem is that X and Y feature some optional mini-games that can only be played with your left hand clamped onto the Nintendo 3DS' circle pad and left shoulder button while your right hand wields a stylus. As you can see in the video above, this is manageable for lefties like me, but it feels about as comfortable as, well, if you're a righty, put a pen in your left hand and let me know how awkward that feels.
Some older 3DS games simply forced left-handed players to deal with controls that required they play as if they were a righty. Others supported the Circle Pad Pro attachment that added a circle pad to the right side of the 3DS. More elegantly, other games have simply cloned the circle pad's inputs onto the A, B, X and Y buttons on the right side of the 3DS allowing for mirrored, lefty-friendly controls.
This is, for example, what the second Dillon's Rolling Western game did to make amends for the first one not having a lefty option. Perhaps a patch could add lefty support for Pokémon? Come on, Nintendo and Game Freak!
How's Miyamoto going to be able to play? Does this man not deserve a perfectly playable Pokémon experience?
We left-handed people have persevered through worse (read: those horrible blunt-edged lefty scissors some of us were supposed to use in kindergarten, as if we couldn't be trusted with pointy righty ones). Oh well.
People of GameFAQs ("Dear Gamefreak, left handed people exist.")...
I feel your minor hand pain.