Counter-examples: the passenger pigeon, the moa, and Mauritius blue pigeon are extinct, primarily due to hunting as a food source.
Other human food species are extinct due to a combination of being a human food source and a food source for invasive species introduced by humans (eg, the Domed Rodrigues giant tortoise).
Famously the American buffalo went from 60 million in the late 1700s to 541 a century later. It was a cheap meat, provided cheap leather, and in order to deprive Plains Indians from a food source, the US government decided not to protect it earlier.
Then there's the collapse of many marine species due to overfishing, most recently the king and snow crab population collapse which canceled the season in Alaska, and the continuing question of the role humans played in the Quaternary extinction event.
Therefore, I suspect your claim isn't so clear-cut.
Other human food species are extinct due to a combination of being a human food source and a food source for invasive species introduced by humans (eg, the Domed Rodrigues giant tortoise).
Famously the American buffalo went from 60 million in the late 1700s to 541 a century later. It was a cheap meat, provided cheap leather, and in order to deprive Plains Indians from a food source, the US government decided not to protect it earlier.
Then there's the collapse of many marine species due to overfishing, most recently the king and snow crab population collapse which canceled the season in Alaska, and the continuing question of the role humans played in the Quaternary extinction event.
Therefore, I suspect your claim isn't so clear-cut.