The GIF Pronunciation Page: Is it “gif” or “jif”? This guy spells out why it’s “jif” like the peanut butter.
CompuServe used to distribute a graphics display program called CompuShow. In the documentation for version 8.33 in the FAQ section, it states:
The GIF (Graphics Interchange Format), pronounced “JIF”, was designed by CompuServe and the official specification released in June of 1987.
There’s more evidence on the page, and it’s pretty compelling. The argument still rages, however. These people over at Everything2 could go either way.