I think that is a glitch in Celebrity's system. As I mentioned previously, if I seriously wanted to make that booking, I would telephone Celebrity or my TA for the correct price.
But also as mentioned, if it was the actual price and I still really wanted to go on that particular cruise, I would use my son's name but he would not cruise. Actually, though, I would walk away and find a better deal!
Or go to Crystal, which has lovely solo ocean view cabins, around 600 guests and always organises a pre-dinner cocktail hour for solos. Oh, and premium drinks and WiFi is always included.