With the decline of predators, such as wolves and coyotes,

Weaken question: Find the conclusion; attack it.

Conclusion: in areas where forest borders on rangeland, deer hunting is an essential activity

How will be attack it? By showing that deer hunting is not essential.
The author builds his argument by saying that deer compete with cattle for food in rangeland. So it is essential to hunt them where forests border rangeland.

Option C says that deer and cattle do not eat the same plants. If that is true, then there is no competition between deer and cattle and hence, it is not essential to hunt them. Conclusion weakened. Answer (C)

deer hunters are not concerned about the prosperity of ranchers
Irrelevant whether deer hunters worry about ranchers.

wolves and coyotes do not prey upon deer only
Irrelevant. We are only worried about the deer population.

deer hunting is popular even in areas where the forest does not border rangeland
Irrelevant. Our only concern is the area where forest borders rangeland.

the deer population may someday be hunted out of existence
Something that might concern us but it doesn't concern our conclusion one bit. We only want to know whether it is essential to hunt deer to ensure that they do not compete with cattle. Possible final outcome of this measure is not the concern of our conclusion.