Allegedly Ruth Handler built Ken's appearance in resemblance to her husband. In February 2004, Mattel announced a split for Ken and Barbie, with Russell Arons, vice president of marketing at Mattel, saying that Barbie and Ken "feel it's time to spend some quality time  apart...
And while the two are boyfriend and girlfriend in the movie, Barbie doesn't seem to feel the same way for Ken as he does for her. Warner Bros. This could be explained by the fact that Barbie and Ken are dolls, and they don't really have a "sexual" attraction to each other.