That's irrelevant. And also it helps both of their careers. Harry Styles likes to play bad boy womaniser. Taylor Swift loves writing about her celebrity relationships. Next.
How is it a publicity stunt? Would've been bad for Justin's publicity considering the good boy image he had at that point in his coupling with Britney. And besides, normally for publicity stunts they're not looking so embarrassed to be seen together. Keep trying.
http://24.media.tumblr.com/f523fbae385581e7111254b171f93c5f/tumblr_mgk2gd9Miu1rp5cado1_500.jpg I'll just leave this here.