I don't know the answer for sure, but the prevalence of farting in Humans is generally a consequence of microbes in our gut digesting our food for us and putting off gasses as a byproduct. There are other reasons gasses end up in your digestive tract, but this is the big one.

I don't know if ants are as reliant on microbes for their digestion as we are, but they definitely have less room for gas in their guts. But then, you'd expect ant farts to be tiny anyway.