Because those were the plants that tasted good and weren't overly difficult to grow. As for the animals, try milking a jaguar. Seriously, it would be too hard to breed a deer that couldn't jump a fence, or to build fences that would hold them. Additionally, venison bacon sucks.
I think they’re on the ball regarding the predisposition of some species to be domesticated. Some species, such as deer, talking birds, etc, can be hand-tamed from early in life, and yet still have to be kept confined in some way. A preceramic culture left the mainland for Cyprus about 8000 years ago and built a village that was inhabited for some period of time. Their origin is known because all the remains of food species in their rubbish tips were from the mainland, and included a species of deer which they’d corral (and maybe preemptively cripple) and slaughter as needed. Of course, animal husbandry of that kind requires agriculture to supply feed.