People root for them because they can. It's a book. You can do what you want with it. It's not the law. So you can like which ever characters you want to like.
I wouldn't say I root for the bad guys, but they are certainly fascinating and they have to be or a piece of literature would cease to be literature and would just become worthless pap. Can you imagine how interminably boring a novel of over 1,000 pages would be if it was just whimsical doings of Hobbits or Elves being nice to one another? It would be truly vomit worthy.
And Tolkien gives us characters who are flawed on both sides, characters who are interesting and complex, like Gollum and Saruman. If he'd just written a black and white novel then it would be rubbish, like some cruddy simplistic 'sword and sorcery' nonsense. Instead he gives us subtlety, shade and light.
I don't care how bad Saruman is. He is a fantastic and utterly fascinating character, more so than some of the Elves who can come across as boring prigs. Thankfully Tolkien gives plenty of page time to his more complex creations. The Shire, Mordor, Angband, Rivendell etc don't exist, so questions over whether I'd rather live in one of them more than another are irrelevant, because to put it bluntly, I WON'T ever live in any of them, I will always live on Planet Earth. Neither Eru nor Morgoth exist nor ever did exist nor ever will, so I can like who I want to like.
In short. There isn't a wrong side, because these are just characters in a book.
