1. Both are hundreds of years old and are said to be immortal.
    
2. Both are mischievous.
    
3. Discord’s past or history prior to his first imprisonment has never been shown or explored, leading many to speclucate on Discord and Celestia relationship prior to that.
    
4. She was the one who wanted him released from stone in the first place and sent him after Tirek instead of Twilight. And was the one who invited him to the Gala.
    
5. She smiles at Discord during the “famous” flowers scene (I say famous because I hate how other Discord shippers (especially Fluttercord) bash this scene or call it “infamous”. I respect their opinion on other shipping. But they should not act so arrogant about it). She even apparently laughs at Discord’s humour. And seems to know that Discord would misbehave at the gala.
    
6. Both their voice actors make teases about the shipping.
    
7. To quote Discord: “What fun is there in making sense?”

@VermiIIion

@CogWeaver
Well, a lot of Celestia and Discord’s history isn’t shown or explored in the show so that gives people a lot of leeway on their relationship before his imprisonment.

That and because Celestia is a bit of a troll herself and loves to cut loose. I mean, she loved his shenanigans at the Gala. Honestly, you can easily make it work. {Twicord would be a much harder thing to sell since they don’t have much of a common ground.}