I wouldn't be surprised if I happen to like Swing when I get to hear it. My musical tastes are very, very diverse - I'm open to anything, really. Whereas the casual listener might burst out laughing when they - for example - hear a Japanese pop song, I can look (listen?) past the unknown language and appreciate the song for its other qualities.
If Sinatra is an example of what you mean by Swing, then yes, I can definitely appreciate that
If there's one genre I don't care much for, it's gangsta rap. That, and maybe the more extreme forms of heavy metal (the types that are all scream, and no substance).