So the person who developed the format and name for it made it to be a soft g like in gin or giraffe. But someone on the internet mispronounced it in their head as people often do for Pokémon or such, and spread it around. This made it popular to say GIF with a hard g like gimmick.
Now, I know it's become a meme to say to originator of the name is wrong about his own chosen name. So now dictionaries say both are acceptable. But still, why did the one that isn't actually accurate to the name made by the inventor gain traction?
It's a name for a tech format, and as a name it has the pronunciation it's inventor gives it.
When the man who invented the GIF, the widely used Web graphic, said that people were pronouncing the term wrong, it started an unexpected debate.
bits.blogs.nytimes.com
You're not gonna go tell Dwyane Wade he says his name wrong. A name is pronounced the way the parent chooses. If one person says "Eesabelle" and the other person says "Izabelle" but their names are spelled the same, you pronounce it as they introduced it and as their parents chose.