@Zennistrad  
That would explain so much…. I hereby accept this headcanon.

So she didn’t mean to send Luna to the moon?  
But rather turn her to stone?  
Seeing how this ended for Discord…
 
Well, I guess that eliminates having to be separated from her…

@TexasUberAlles  
… I could see this.

@TexasUberAlles  
… Nice.

I think the dirty secret that they’ve been keeping since Luna’s return is that Celestia didn’t send Nightmare Moon on her thousand year vacation… Luna did. Celestia tried to use the Elements to break NM’s hold on Luna, but couldn’t use them by herself; Luna wasn’t powerful enough to separate herself from NM, and didn’t want to take the chance of her gaining access to that power, so she provided the Harmony to complete the circuit to banish herself, and NM along with her.
 
…Celestia wasn’t hard enough to banish her sister, even for the good of all Equestria. Her sister was hard enough to banish herself, knowing she would leave her sister behind to live with the guilt for a millennium.

Muh headcanon says that to be able to fully control the elements, they need a given amount of magical power to begin with. That is provided by the mane six, currently, and back then, it was given by Luna and Celestia. However, when Luna gone insane, obviously it was only Celestia using it against her. She alone however wasn’t strong enough to be able to control of the elements’ power. So, while her original intent was stripping Luna of her Nightmare powers, which the elements actually did, but then they started picking apart Luna herself too. In a desperate final attempt to save her sister, she directed all that raw magical power to the moon… But unfortunately it took Luna with itself.  
(And also this is my explanation for Celestia’s multicolored mane. The power overflow tainted it.)

@Zennistrad  
That could work too.

@Psyga315
 
I think the reason the Elements didn’t work properly is because Luna was the other bearer for them.
 
By turning the Elements against her sister, Celestia was destroying the harmony between her and Luna.
 
This not only weakened their power, but severed Celestia and Luna’s connection to the Elements permanently.

I don’t get it…

I’m pretty sure she just lost all hope of successful negotiation and went all “just bucking do something with this insane sister of mine, Elements, she’s killing my subjects out of madness”.  
_{Obligatory whine about using “to” instead of “into”}

@Zennistrad  
He’s implying that the elements didn’t go as planned. They would have befriended her and turned her good, but because the other element bearers weren’t the “right ones” (like the discorded ponies), it backfired, but not to the point where it totally fizzled. It worked, but not the way Celestia wanted it.
 
If that’s the case, I now have a new found respect to Celestia.

Wait, if Luna was sent to the moon because of Discorded Celestia, how was the there to turn Discord into stone?

@MrThumbsup  
Well, not literally…

@Psyga315  

So… Celestia was Discorded?

I see what you did there.