Why I dont like music? I'm not sure, if I'm alone, but I never liked music, any kind of music. It never made me happy or sad. Actually it never ever had any effects on me right from my childhood days. My iPod(received as a gift) is filled with audio version of movies and dramas, but never songs. 

Is it some kind of mental illness?
I wouldn't call it a disorder, unless it significantly affects your life. Not enjoying music or not being able to produce music is known as "amusia". It probably has to do with differences in perceiving pitch [1]. It can also occur in people with recently fitted hearing aids or cochlear implants [2].

If you are interested in this, there is a chapter about cases of amusia in Oliver Sack's book Musicophilia [3].

References:
[1] Liu F, Patel AD, Fourcin A, Stewart L. (2010). Intonation processing in congenital amusia: discrimination, identification and imitation. Brain. 133(Pt 6):1682-93. doi:10.1093/brain/awq089
[2] Cooper, W., Tobey, E., &amp; Loizou, P. (2008). Music Perception by Cochlear Implant and Normal Hearing Listeners as Measured by the Montreal Battery for Evaluation of Amusia. Ear and Hearing, 29(4), 618. doi:10.1097/AUD.0b013e318174e787
[3] http://www.oliversacks.com/books-by-oliver-sacks/musicophilia/