When Kurt was little he used to sing with his mom, and he loved it. It used to make him feel really good and very, very special. So when his mom died he started to take singing a lot more seriously than he did before. Three weeks after she died he started practicing, and he quickly realized that it was one of the few things that actually made him feel better.
Singing had always made him feel wonderful, even after his mom left him. Sure, his dad must have thought that it was weird that every time Kurt got upset or angry he would sing out his feelings, but if it worked it worked. When he got to high school he joined Glee club even if the teacher was creepy—if he believed in God he would be thanking Him for Rachel Berry, who got the guy fired—and the other kids picked on him more. They were going to pick on him anyway, just as they always had. So what was the point in trying to go under the radar, when it was practically focused on him?
As it was the only way he could really express himself, Kurt became rather good at singing. In his opinion, he was the most talented person in all of Lima, Ohio—which actually had competition for him, surprisingly enough—and he was ready to prove it as soon as he got out of high school. Until then he would deal with all the torment that came with it.
After all, most of the bullies at school would be lucky to be hired by him in the future. Maybe he would go out of his way to employ them, just so they can remember how crappy they treated him when they get turned down for a promotion again. That was a bit mean, but then again so was throwing slushies and pee balloons at him. That was seriously messed up, and so disgusting that Kurt wouldn't ever forget it, so maybe he deserved to be bitter about it in his imagined future.
He never expected for the bullying to get as bad as it did, but then again he never expected to meet Blaine Anderson—or Blaine Warbler, as his friends have taken to calling him—and fall in love for the first time. They had their ups and downs, like every couple did, but Blaine was like him; he liked to sing about his feelings, he had been bullied, he got him.
When they had their downs they sung about it, and when they were happy they sung about that, too. When Kurt had to face his second loss in life, the loss of his step-brother, it was no surprise to anyone that he sung about it. They even sung with him, because his friends also sung out their feelings sometimes.
Music was something that made people feel better about themselves, about their situation, about anything that may bother them. Because what better way was there in getting over sadness than knowing that you're not alone in your struggle?