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Interviews with Guns N' Roses band members suggest that between 1994 and 1996, the band sporadically began to write and record new material, most of which, according to Slash, had been written by Rose. Rose has stated the exact opposite in the open letter on the official Guns N' Roses website, that the album was mostly a "Slash album" and Rose was allowed very little input into the album. At the time, the band had intended to release a single album with 10 or 12 songs.
Regarding the dysfunction of the band's recording at that time, Rose is quoted as saying, "We still needed the collaboration of the band as a whole to write the best songs. Since none of that happened, that's the reason why that material got scrapped."
In December 1994, Guns N' Roses released a cover recording of the Rolling Stones' "Sympathy for the Devil". The song appeared in the film Interview with the Vampire, on the movie's soundtrack and was also released separately as a single. It is the final Guns N' Roses single to feature Slash on lead guitar, Duff McKagan on bass, and Matt Sorum on the drums. It also featured Paul Huge on rhythm guitar, whose presence on the track and in the band created great tension between Rose and Slash, as Slash disliked Huge and felt he had no place nor the 'chops' to fit in G N' R.
The recording of "Sympathy for the Devil", as well as tension between him and Rose, led Slash to quit the band officially in October 1996. He was replaced by Nine Inch Nails touring guitarist Robin Finck in January 1997, who signed a two year contract with the band in August 1997 making him an official member. Slash's departure was followed shortly thereafter by Matt Sorum, who was fired in April 1997 and then by bassist Duff McKagan, who resigned from the band in August 1997. As such, all of the members who had taken part in the recording of Appetite for Destruction (aside from Rose) had departed from the band.
So basically, they were not getting along and wanted to go in different directions. The "Sympathy for the Devil" recording was the last straw. Neither of the two, especially Axl, are very good at solving problems and can be very stubborn. They wouldn't work the problems out, so it blew up into a huge fight that they still continue. Slash has stated he's willing to reunite if Axl apologizes first. But Axl will never do that. Slash could apologize, but he won't do that either. If neither one of them will step up and be the bigger man, they'll never get anywhere.
Source(s):
Wiki and me