I'm sure they are wonderful hunters and fishermen under normal circumstances. But in a SHTF-WROL-collapse kind of scenario, it's not normal circumstances. Food supply lines have stopped serving the society, so EVERYBODY IS LOOKING FOR FOOD. This is the main difference.
When society first collapses, people will eat whatever is in their fridge and pantry. After that, people with guns will go hunting, while people with fishing poles will go fishing. Everybody and their grandma will be in the woods hunting. Anybody with a gun, even pistols might be out trying to hunt. What other option do they have? Around half of the households in the US have either a gun or fishing gear. They will all be doing their best to survive.
REASON #1 - THERE WILL BE TOO MUCH COMPETITION FOR FOOD
When you have so many people competing for the same food, fish and game populations will dwindle drastically. The rivers in Europe were fished out hundreds of years ago. By 1930, deer population in the United States dwindled down to 300,000 as a result of unregulated hunting and the Great Depression (today it is 25 million). And that was when our population was only 100 million. Now our population is over 300 million. Can you imagine how we will decimate fish and game populations if nearly all of us transition to subsistence living overnight? No matter how good of a hunter or fisherman you are, it is foolish to assume the supply of food will always be there. It is better to store up food and make plans to farm, rather than rely on hunting and fishing.
REASON #2 - CIVILIZATION WAS NEVER BUILT BY PEOPLE THAT RELIED ON HUNTING AND GATHERING
There is a reason why hunting and gathering was the earliest stage of human civilization evolution - it was the suckiest form of living. People advanced from that into an agrarian society, because farming was more stable, reliable, and easier. Why do you want to go back 50,000 years in time, when you can go back just 500 years in time? Plus, it allowed extra time to work on other things, like education, trade, and banking. If society collapses and you have any desire at all to get life back to a civil state, you'll prepare for a lifestyle that involves farming. If you choose to hunt and gather, most of your time will be spent gathering food. If you choose to farm, you will have some extra time to educate your children, set up water wheels, make radio broadcasts, go on trade caravans, etc. Doesn't that sound much more awesome?
Would you really wanna be like these guys???
REASON #3 - YOU CAN SAVE LIVES IF YOU LEAVE THE FISH AND GAME FOR OTHERS
Like was previously discussed, many many people will be in the woods trying to survive off mother nature. Every fish you don't catch is a fish that can nourish a starving person. Every deer you don't shoot is a deer that can provide nourishment for a starving family for a month. You may never see these people, but it will be very likely they exist and they are in the same forest as you looking for food. Now, if you are in an extremely remote location, it probably won't matter, so shoot and fish all you want, but most places in the lower 48 will meet this criteria. If you can leave food in the wilderness for others to eat, you just might save their lives and that could come back around to help you, because you might become friends and trade partners later. You can form an alliance. The good people living in the wilderness might have to deal with the threats of the gangs and warlords that have risen up in the populated areas. The more people that can join your extended community, the better. And you know that the others out in the wilderness hunting are likely good people, because they have a firearm, but instead of using that weapon to steal from others, they have made the moral decision to use it for hunting instead. The people that go into the wilderness will be the 'go-getters', the 'self-relient', the ones who choose to provide for themselves rather than those who choose to let others provide for them, or worse, the ones who choose to steal to provide for themselves. So, those are the people you want to have on your side when society has collapsed. It is worth leaving fish and game in the wild in order to save some of their lives.
PS: I'm not a wildlife expert, but in regard to fish and game populations, they will take a big hit in the first 2 to 5 years. By that point, everyone who was going to die, has died, and everyone who was going to figure out a way to live, has figured out a way to live. Things will become more stable. After that, game populations will explode and mother nature will reclaim a lot of what man has taken. So, after 5 years or so, feel free to hunt if you so desire. Fish populations might be a different thing though. I imagine people will settle along streams and rely heavily upon fish. It probably depends on the water system though. I think some water systems will be fished out, while some will flourish again after that 5 year mark.