Firstly, in the page you linked to, Kakashi says "No matter how far he fell, the Third always looked upon Orochimaru with affection. I think I understand now what he went though those years ago." No mention about Sasuke being his favourite, only that Kakashi still cares about Sasuke.
Up until the Chuunin exams, Kakashi treated all three pretty equally.
So the 'favouritism' is because he trained with Sasuke for the month leading up to the third exam.
3 points here.
1. Sasuke was facing Gaara (you know, looking-forward-to-killing-you Gaara?). Naruto was up against a fellow leaf nin who, since Naruto was not a main branch Hyuuga, was not inclined to kill Naruto.
Gaara was more likely to try to kill Sasuke than Neji was to try to kill Naruto.
Gaara was more likely to succeed if he tried to kill Sasuke than Neji was if he tried to kill Naruto. (Naruto had higher durability thanks to Kyuubi; Neji wasn't really a one-hit killer.)
Therefore Sasuke was more likely to die without special training.
2. Kakashi did not tell Naruto, "Nope, not helping, sort yourself out." He gave him a teacher. A teacher of basics. Which Naruto really, really, really needed help with. (Working on the assumption that Kakashi did not know Jiraiya was in Konoha - if he did then he gave Naruto a stronger teacher than he gave Sasuke.)
3. Naruto is not a lightning type; besides chidori was created as a response to rasengan, which Kakashi doubtless figured Naruto would learn in time - just not in the space of a month.
(There may also have been an element of protection against Orochimaru, but Kakashi clearly believes he's significantly weaker than Orochimaru, so I don't know how teaching Sasuke one jutsu is supposed to help.)
Mostly point 1 though: Kakashi taught Sasuke because he didn't want any of his students dying and Sasuke was at greatest risk at the time.