why do you ship S/C ?

I ship them because they sit below the radar. Very underrated and Christine needs more love (she was an amazing character, but the writers never seemed to give any of the side characters a chance). She cares for Spock, she'd never take advantage, she loves Spock for who he is. To me, that's a wonderful pairing.

"I'm in love with you Mr. Spock. You, the human Mr. Spock, the Vulcan Mr. Spock..I don't know why but I love you. Just as you are." -Christine Chapel "The Naked Time"

Basically that scene! From the very beginning she understood him, that his human side hurt him and how he had to control his feelings. The actors played it so well too. You could sort of feel the longing in that scene. Chapel was not, as others have described her, a stalker or a pathetic, hysterical woman in love. She was intelligent and compassionate, and above all cared for every member of the crew and kept herself together after finding out the love of her life was dead and replaced by a machine. She's actually a remarkable woman, I think.