Most of the characters on Glee have a very basic reason that motivates a lot of their actions, that is explicitly stated.
Will is afraid of never living out his dreams and ending up like his parents (or April Rhodes).
Emma has OCD from a childhood incident.
Santana is *****y so much because she's afraid of her own feelings for Brittany and the fact that she's probably a lesbian.
Rachel was alternately spoiled by her dads and is unpopular at school, and doesn't want to end high school without some grand accompishment to show for it. Her diva-ness is probably a combination of being spoiled rotten, and a shield against her insecurities.
Kurt is a little bit like Rachel, as far as the "diva as a defense mechanism", and he's probably also spoiled by Burt (which is understandable on Burt's part, as he lost his wife and Kurt is all he has). His comment to Blaine about having to scream to get noticed is probably also telling. He dresses outrageously and plays the diva because, like Rachel, he thinks it's better than just being outright ignored, and also as a "hate on me, haters", kind of middle finger.
Sue was ****ed up by her mother, who usually wasn't around, and when she was, only ran Sue down and bullied her.
Quinn has insecurities about her "Lucy Caboosy" past and has gone through a teen pregnancy, giving away her baby, and being kicked out by her father, and defends her status and popularity so obsessively because she feels like it's the only thing she can hold onto. However, this isn't going to last past high school, and that leaves her terrified of the future (and also determined to be the reigning Queen for as long as she can in the here and now).
Blaine tries to be picture-perfect in every way, handsome, well-mannered, suave, charming, popular, inoffensive, etc. probably as his own defense mechanism from his background of being bullied. He comes across as almost a little too calm and collected, probably a little repressed. Dalton is probably the first place he found where he felt safe, hence his reluctance to "rock the boat" and go against its conformist atmosphere.