There are many reasons why people in Telangana want it and people in other parts of state oppose it.
First reason is water, The catchment area of Krishna and Godavari is around 79% in Telangana, but telangana gets only 19% of the water. In a separate state, The water share in Andhra is going to decrease, The people there definitely don't want to lose the water they are getting.
Second reason is Hyderabad. The revenue out of Hyderabad and its surrounding areas is around 45% of the state's revenue. Telangana people say that, Hyderabad is the heart of the area since the nizam days. Andhra people say that we have developed Hyderabad and we won't part away with it. (The revenue from remaining areas of telangana is 16% and not even that amount is used in the development of the area)
Third and important reason for the opposition of Telangana in other areas, The politicians from seemandhra have huge financial interests in and around Hyderabad(Factories, Lands in the name of Binami) and the fact that they wont have any say in the dealings and contracts in Hyderabad.
I would add a personal experience of my father in this matter: According to a G.O issued by Govt of AP, Only people from Telangana should be allowed to take up posts in the area, There was a post of vigilance officer available in Hyderabad Metro water supply & sewage board so my dad went and applied for the post and was the only eligible person who applied for the post but a person from seemandhra was given the post by the MD of HMWS (who himself was from seemandhra). If such kind of partiality is shown by them. why would we want to be part of a unified state.