Did Eccleston ever give a real reason as to why he left? Why is he soured on the whole thing?
There's a lot of reasons, it seems, but the key ones appear to be...
1) He's a very, very 'method' actor in general and was terrified of getting typecast by the show. He said he'd never have done it if it was anyone but RTD, who he'd worked with before.
2) Nobody working on the show had ever made a show like Doctor Who before - sci-fi with effects and things like that. RTD said in their first week they were already three weeks behind - they'd planned to film a certain number of pages per day and realized 3 days in that it was wayyy too high. It didn't help that the first story filmed was Aliens of London/World War Three - pretty complex episodes with tons of massive, unwieldy prosthetics. Series 1 seriously barely got made at all. It was hell on set, supposedly.
3) Eccleston was the kind of actor who liked a calm filming environment... and all the problems caused him to have a really fraught relationship with Phil Collinson, the on-set producer, and other members of the crew. Collinson is pretty famous for being a sort of 'no shit' kind of guy, though - it was in the newspapers that when he moved to Coronation Street after Doctor Who he ruffled a lot of feathers, too. There's been suggestion Eccleston was perhaps a bit of a prima donna, as many great actors are, so it's no surprise those two clashed... but he was also amazing... Sadly, Doctor Who is a world of constant changes and rewrites and dubs and things like that. He's spoken of his hate for the dub - but with effects and things, the original sound would often be lost. Presumably Tennant and Smith don't despise trying to recreate their original performance as much.
By the time things got better and the team got a handle on how to successfully make this kind of show, relationships were already frayed and ruined. Eccleston didn't even wait around for Tennant during the regeneration - where Smith snuck in and did his scenes at the same time as Tennant, Tennant's stuff was filmed later and Eccleston didn't want to be there.
Despite all this he has said he never intended to do more than one series due to reason 1... but I'm sure 2 and 3 factored in. You can see his disdain in interviews even as early as the launch party for Rose, when they were still filming.