Because one group generally operates in a fantasy world of how things should happen and the other has been proving for over 100 years that their method works.
Generally speaking the people with the most skin in the game are more likely to have a vested interest in a positive outcome. To most animal rights people and anti hunters the majority of wildlife to them is a brief interlude of “that’s neat” on a walk through the woods or a video on a screen. They are so far removed from nature they don’t have the faintest idea of what is required to keep animal populations sustained at healthy levels.
Completely removing hunting from the equation results in one of two things, either a new predator is reintroduced to an area to control animal populations or they proceed to multiply to the point that they detrimentally affect their habitat leading to a crash in populations.
Take for example here in PA, there are an estimated 1.5 million deer and hunters kill on average around 400,000 deer a year which keeps the population in check. Now imagine hunters stopped killing them, in the first year the population would jump by 600,000 based on the deer not killed and their fawns bringing the total to 2.1 million. The following year they are up an additional million to 3.1 million and the deer are putting a severe strain on their environment. Other animals start to suffer due to the deer eating all of the understory, does start aborting their fawns due to lack of food, car accidents and diseases start taking a larger number and you are one severe winter away from a huge population crash that takes decades to recover due to the greatly diminished habitat.
The other alternative is predators, people already have issues with coyotes so how would they feel about the 20,000 wolves or 8,000 mountain lions required to harvest as many deer as the hunters do?