The CIA feeling they were being questioned about their work, and the White House folks feeling like they weren't getting enough info, and that the press was getting too much.
The problem is, that neither group acted like adults, for whatever reason, and worked it out face to face. It ended up being a behind the back, "gotcha game" for the two sides. Not a great way to run a government.
I think when Bush leaves office George Tenent will probably write a book similar to the one Louis Freeh wrote about the Clinton years at the FBI.
For more on the infighting, and whole proceeding, here's a link to Time Magazine's article on the indictments, it's pretty balanced, which isn't always the case with them.