Man is a scavenger who augments his diet with nuts and fruits, in case we've forgotten. This is why we mostly eat dead animals, some considerable time after their death (21-28 days for US prime corn fed angus). We get our veggies by eating the animal's stomach contents, henceforth almost always vegetarians, as we can not digest greens unaided; haggis entertains this concept to this very day. Since the "invention" of fire and cooking, things became a lot more culinarily challenging
Fish is a very recent addition to our diet and according to some people I've spoken to, I'm all wrong about poultry being part of the animal kingdom, after all...
Feh, our immune system and toxin tolerance is far inadequate for us to be proper scavengers. We're far more prone to food poisoning than most rodents, cats, dogs, bears, raccoons, vultures, crows, etc. And, although the "aged" meat example is real in modern usage, a lot of cultures, particularly pre-refrigeration, also but a lot of value on freshness, and we came up with all sorts of spices and preservation techniques to reduce the intrinsic distaste for meat that's been sitting around. Also, although yuppy steak dealers may push aged meat, they do it in sort of an abstract way; in supermarkets, at least in the US, people go for the red, fresh-looking meat, to the point where companies inject carbon monoxide into the meat before sealing it in plastic, so it continues to look red and bloody/fresh for longer.
We're certainly not good ruminants either, particularly in the grass digestion department but also in regards to some grains, but I don't think our ancestors were equipped to have been carrion-eaters. Our molars are good for some level of nut and grain crunching, and we seem to have a strong taste for fruits and legumes. Digestively, I don't think we have any problems with fresh meat, either, although cooking probably led to a big meat-directed shift in diet because it was able to eliminate parasites and pathogens... and it does open us up to some grains that are inedible without treatment, both from a digestion standpoint and by denaturing toxic proteins and such.
It's surprising we have more of an aversion to eating bugs than most primates. I wonder if that's a more immediate cultural factor because insects are an indicator of unhealthy storage conditions for food, more than because they're not good for us to eat.
Unfortunately, it's pretty much in the nature of being an animal that we can't live without exploiting something. I can understand the vegetarian rationale that it seems more noble to live by only exploiting things that don't have enough awareness that they'll miss being alive, though. But not enough that I eschew tasty meat.
I suspect that over the next few hundred years we can get to the point where we can make engineered "meat-fruit plants," and at that point that rationale might shift me away from meat consumption, particularly since large-scale animal farming has gotten rather cruel, irresponsible, and just full of bad practices from overcrowding, questionable overuse of antibiotics and unnatural dietary supplements, poor waste management, and selective breeding to the point where genetic diversity in livestock (and vegetable & grain stocks, for that matter) is absurdly low.
As long as I'm going off on tangents, I'll also mention that most of the arguments against GMOs also apply to things that are done in both plant and animal farming all the time: producing artificial stocks that have stupid characteristics, and eliminating the established evolved stocks from the wild. Being an overall cynic, I am frustrated that the alternative to this, organic foods, tends to be plagued by irrational ideas like "it's good to be a luddite" and "any modern farming technique is inherently bad, including sterilization, refrigeration, and sensible packaging" so I'm not too big on that... Organic farming seems to frequently take the attitude that all modern agriculture is inherently bad, even though modernization, while certainly causing some horrible problems, has also reduced the levels of foodborne illnesses dramatically since the 19th century and has allowed us to scale up food production to the point where it's much more economically feasible for modern populations. Choosing between mainstream agribusiness and organic is as bad, at least in the US, as choosing between Republicans and Democrats: they're all based on fanatical loyalty to poorly-thought-out, naive "platforms."