We didn't really get a feeling that Kirk & Carol were one of the great romances. It seemed to me that it was a more casual relationship that ended up with a surprise package. Maybe carol wanted a child and stopped using whatever future birth control she was on. She might have selected Kirk for the very reason that she knew he wouldn't do the "honorable thing" and try to marry her. His line "I did as you asked. I stayed away." makes it quite clear that it was Carol who didn't want Kirk around her son. She saw David as hers. It's possible that she simply saw Kirk as a friend who she chose to be the sperm donor.