I'm going to run down the Steve Rinella talking points here:
Point 1: Hunting and Fishing license/tag sales basically fund state fish and wildlife agencies (which manage conservation efforts). Folks who drive through Yellowstone for a day or two and then rail against hunting don't help. Hunters that are buying tags that cost between ~$1000 and over $100,000 (governor's sheep tags), buy fishing licenses, and pay additional taxes on firearms and fishing gear fund the agencies that actually conserve wildlife. Hunting participation numbers are going down nationwide. The money has to come from somewhere. Running down hunters is basically cutting off your nose to spite your face if you like being able to see wild places with lots of animals for free.
Point 2: If humans live somewhere, we alter the environment. We build roads, houses, farms, yards, schools, towns, dams, bridges, etc. and drive vehicles all over the place. Additionally, we want our kids, pets, and stuff to be safe so we build a lot of fences. All of that alters the ecosystem. Grizzlies used to exist in much higher numbers across the US because the environment would support them (one factor is that we essentially eliminated buffalo, which, IIRC, frozen buffalo carcasses were a significant early spring food source). If we alter the ecosystem (by existing in it), the mature thing to do is to manage it from there on out. That's what state game and fish agencies do, and they are pretty good at it.
Point 3: Specifically regarding species management, some species "regulate" their population numbers better than others. If we don't help manage population numbers, they tend to expand quickly when conditions are good, and then crash catastrophically a few seasons later when they have over-utilized food sources and conditions are bad. Right now hunters pay for the opportunity to help manage those numbers. If we stop hunting, we will have to pay game agency employees to kill animals.
Point 4: Wolves and Grizzlies get all the "love" from anti-hunters, but they really aren't in a compromised population situation, there are populations that are facing much bigger challenges that the anti's don't give a shit about. Sheep, Woodland Caribou, Sage Grouse, etc. There are about a dozen caribou left in the lower 48. "Biologists who work with the Kalispel and Kootenai Native American tribes are concerned that the caribou will disappear before they can act, and urge more aggressive support from the public and agencies. “Wolves and grizzly bears suck up a lot of the money,” said Bart George, a biologist with the Kalispel tribe. “Where is the support for this charismatic species?”"