Why doesn't Adam Lambert like clay aiken?

Answer 1

Adam does not dislike Clay Aiken. Clay actually started a bit of a feud in 2009. Clay basically trashed everything about Idol on his subscription-only message board, and said Adam's "Ring of Fire" made his "ears bleed" and was "Contrived, awful, and slightly frightening". When Adam was asked about this he said "I don’t know Clay. I’m glad he’s getting headlines now though, because he wasn’t before."
Clay then issued an apology a day later. "I do apologize to Adam for my colorful (and negative) choice of words. I hope he can forgive me," Clay wrote. "I imagine he doesn’t give a damn! :-) God knows he shouldn’t."
After Season 8 of Idol was over Clay went on at length about how Idol voters made the right choice in Kris Allen, despite Adam's vocal chops and popularity and said that Kris seemed more "likable" than Adam.
After that Clay has taken every opportunity to make negative comments about Adam. The only other comment Adam has made about Clay was on Bravo's Watch What Happens in May 2012. When Andy Cohen asked Adam to say "three nice things" about Clay when playing the show's traditional game of "Plead the Fifth", he was at a loss for words and replied "Can't think of any," to which Cohen asked: "Want to plead the fifth?" "No, I just can't think of any nice things," said Adam, laughing.

I would say that basically any bad blood is more between the fans of Clay and Adam, who won't forget the negative things Clay continues to voice. I would also say if there is any real 'dislike' it is more Clay's not liking Adam.