He grew incredibly disillusioned with the people running Dr Who at the time. Despite repeated attempts on his part to get people to treat others better, things never changed according to him. He also had a very poor working relationship with John Barrowman, who was repeatedly accused of sexually inappropriate behaviour (eg exposing himself to his co-stars unprompted, supposedly as a joke). Noel Clarke has also been accused of inappropriate behaviour.

Eccleston did not want to work for people who in his view were responsible for the mistreatment of his colleagues on set. He was open to returning to the role, but never with those same people still in charge.

On top of all that, he initially just shut his mouth when he left, not naming names. Then the BBC published a statement saying he was "overwhelmed by the tv shooting schedule" and that he was tired, which is killing for an actor's career. He had a tough time getting roles after that, and basically was forced to work for American producers because nobody in the UK would touch him.

Tennant mentioned that though their interaction was brief, Eccleston was very amicable towards him when Tennant took over.

Eccleston can be petty, but it doesn't seem like he ever was towards someone who didn't deserve it. And given how the BBC and the producers mistreated him, he's been shockingly fair imo.

You'll find the general opinion of Eccleston runs contrary to yours, and manages to do so without the pottymouth.