Anon: “Celestia, why are you afraid of a harmless chicken? You just scared away a very dangerous monster a few moments ago!”
 
Celestia: “Yes… but he… was not… a CHICKEN!”
 
Anon: “But why chickens, of all things?!”
 
Celestia: “Well… I had some REALLY bad experiences when I was a foal…
 
 
Considering how brave and selfless Celestia usually is, I think her alektorophobia is forgivable :-)
 
 
And concerning what she says about Discord in the first panel:  
We know that Discord is childish, short tempered and vindictive. So why is it, that after a thousand years of petrification, he does not immediately take revenge at the pony who inflicted it upon him? Why is it, That he doesn’t petrify, torture or humiliate Celestia? He had enough time while the Mane 6 were in the maze. My answer to that is: If he could have, he WOULD have!  
Even if Celestia needs the Elements of Harmony to seal Discord away, he doesn’t seem powerful enough to confront her directly. In “Keep Calm And Flutter On” she puts a spell on the Elements, so he can’t steal them and he was never able to break it. And in “Twilight’s Kingdom” Discord can’t just snap his fingers and serve the princesses to Tirek on a silver platter. Instead he must first help Tirek becoming strong enough to confront them. It seems that the worst thing Discord can do to Celestia is stealing her tail and putting her in a clown costume. But if she’s really willing to get violent… well… I guess Dissy would end up as a fried sausage XD  
And about the MLP Movie: Those petrification-orbs were a special magic weapon and if Discord were there during the attack, he most likely would have been petrifyed, too.