This quest line is to collect meat, not consume it. You can collect meat by killing the various animals roaming the map. When you are close to an animal you should be able to hear them or see an icon if you have visual sound effects turned on.

Meat is a good item to have because it restores 15 health and can be used to craft the hunters cloak. Meat heals faster than bandages and can heal you all the way to full health.