[denethorthefirst]

Thats not necessarily a contradiction. It could also simply mean that Hobbits hunt for food, but not for entertainment (sport). Hobbits are depicted as a simple but good-hearted people: killing just for fun would be atypical, but they are clearly meat-eaters and have no problem with killing animals in order to eat or otherwise utilize them (for example to produce leather).
But ... we have to keep in mind that the Shire is in a lot of ways an idealized version of the english countryside, and killing for fun (for example fox hunting) definitely was and still is a part of english country-life - so it is at least a possibility that the Hobbits maybe hunted for fun after all.