If it weren't for Andy Milonakis tweeting that "choosy web designers choose GIF," I'd never be able to remember how to pronounce the damned file extension. Are Andy and I really pronouncing it correctly though?

According to the folks at The Atlantic, yes.

Some digging into English etymology and pronunciation standards may have yielded mixed results, but there are two pieces of evidence discovered by The Atlantic's staff that can serve as reassurance that we're pronouncing things correctly. The first is found in the FAQ section of a CompuServe graphics display bulletin called CompuShow:

"The GIF (Graphics Interchange Format), pronounced 'JIF,' was designed by CompuServe and the official specification released in June of 1987." [This means that] in their very own document, the GIF's creators indicate their preference for the soft-j.

The second piece of evidence was found in another very early FAQ on the topic:

Choosy programmers choose "gif" or "jif"?

The pronunciation of "GIF" is specified in the GIF specification to be "jif", as in "jiffy", rather then "gif", which most people seem to prefer. This does seem strange because the "G" is from the word "Graphics" and not "Jraphics".

So there you have it: The peanut butter pronunciation is technically the correct one to go with.

It's ok if you're a rebel and decide to go against what the creators of the GIF established anyway though, because the Oxford English Dictionary has your back as it declares both both the hard g and soft g pronunciations correct. [The Atlantic]