According to this question, the Mages guild got disbanded because people think they were involved in the Oblivion Crisis and that they don't allow necromancy. It said that when Hannibal became Arch Mage in the Elder Scrolls IV Oblivion, he banned necromancy, even the founder of the Guild hated necromancy. So why is necromancy banned in the Guild? Did the College of Winterhold get involved in necromancy too?
For one, most races of Tamriel don't like having the remains and/or souls of their ancestors / family / loved ones messed with.
Conjuring and binding spirits, and reanimating corpses is said to corrupt the souls of those who practice the dark arts, leading them further and further away from what the populations deem acceptable. It is also notoriously difficult to control - many who practice necromancy have lost control over their undead minions, leaving everyone else to clean up their mess.
Proponents often argue that the lines drawn between the schools of magic are not so clear cut (enchanting uses bound souls, for example), but there are counter arguments that what little bits of necromancy the other schools touch on are far less dangerous.
The UESP Wiki has a lore page on necromancy that goes into further details on the history of necromancy throughout the Elder Scrolls universe. And the Elder Scrolls Wiki has a page on a book that appears in both Oblivion and Skyrim, The Black Arts On Trial, that details the arguments for and against Necromancy that ultimately resulted in the Mage's Guild banning the practice.
The College of Winterhold, being independent from the Mage's Guild, has historically been somewhat accepting of necromancy.