Humans were the reason, on all continents.
https://ourworldindata.org/wild-mammal-decline
"By around 10,000 years ago we see a huge decline of wild mammals. It’s hard to give a precise estimate of the size of these losses millennia ago, but they were large: likely in the range of 25% to 50%."
"It wasn’t just that we lost a lot of mammals. It was almost exclusively the world’s largest mammals that vanished. This big decline of mammals is referred to as the Quaternary Megafauna Extinction (QME). The QME led to the extinction of more than 178 of the world’s large mammals (‘megafauna’)."
We lost the biggest animals because those were the ones we hunted. If the reason were to be the fire (which sounds ridiculous), it would have caused the extinction of mammals of all sizes, not just the largest ones.