Personal theory here is "big foot" is some proto human ape. There are fossil remnants of tool making humanoids in Africa that greatly resembled apes. Such as Australopithecus Bosei, who where divergent evolutionary branches from the common human ancestor and eventually became extinct.

Its also known modern man was not the first homo species to venture out of Africa. Homo Erectus is known to have moved as far as China.

I theorize that bigfoot is a human evolution divergent that had been successively pushed into more remote areas by the much more dangerous humans. To exist without official detection for so long they must exhibit an intelligence greater than the chimpanzee (an animal known to exhibit self-awarenes.) Also curiously there have been plenty of sightings but never reports of attacks on people. Could be that the attacked never live to tell the tale or could be the bigfoot knows better than insight human wrath.

I would guess they are social creatures, and fully aware of how incredibly dangerous humans are. It doesn't take much intelligence to realize humans tend to try and kill everything they see, and are far too strong to be driven back. Its why even very large predatory mammals are wary of humans, those that were not met natural selection very quickly. Its also possible like neaderthals they bury their dead, and thus would make discovery of specimens nearly impossible. Its possible they even recover the dead that might have been killed by human hunters or traps or accidents. They must also be a very rare animal, as ecosystems would have trouble supporting large populations of such a large creature, especially with such limited ranges due to human encroachment.

Its quite a misnomer that even human cites are animal free. We expect squirrels and mice, but there are cases of animals as big as panthers going unnoticed in heavily urban areas for very long periods of time. They were eventually tracked and delt with, but the idea that a panther Animals exhibit an elusiveness and cunning that at times can be surprising.

The eyewitness accounts are generally quite consistent, and even more remarkable, there are corresponding accounts from other areas of the world.

Another factor, if bigfoot is a human evolutionary divergent, DNA sampling of hair or tissue found would be hard. Not becasue of bad DNA, but becasue it would be so close to human most scientists/DNA techs would dismiss genuine results as contamination, or a hoax. The same would hold true for hair samples, as they would likely be very similar to human hairs.

However until a specimen is found and verified by independent researches this debate and theorizing will continue on forever. It might be a terrible thing if bigfoot is ever proven to exist, as it would spark a spree of attempted poaching that would make the discovered animal extinct in short order.

And if it does exist, perhaps the Bigfoot knows this, and thus why its so careful to avoid detection.