It should be pronounced as JitHub. At least GitHub team wants us to call it like that. Yet I prefer to pronounce it as GitHub. It's more of habit than a logical reason.
Well, here's some logic that proves that the Github product team must consist of a bunch of foolish idiots - literally (you'll soon see what I mean.)
First of all, "jit" is another term for ejaculation.
Secondly, the word "git" (pronounced "/git/") is informal, British slang for a foolish or unpleasant person. Linus Torvalds gave that name to the version control system, after tons of work on the Linux kernal was pending or completed and was not being properly organized by him after the amount of developers on the team increased. They needed a "stupid content tracker", and he even said in an interview, "I'm an egotistical bastard, and I name all my projects after myself. First Linux, now Git."