The difference of opinion is primarily about what constitutes a valid conclusion from the available evidence for Bigfoot. The pro-Bigfoot side seems to be erring on the side of seeing possibility in a scarcity of evidence, a scarcity that is readily conceded, while the anti-Bigfoot side seems to be engaging in the fallacy of trying to prove a negative, i.e., to demonstrate scientifically the impossibility or at least sheer unlikelihood of Bigfoot.
I think the pro-Bigfoot side is taking pretty much the common course for a phenomena for which there is practically no evidence, and certainly no hard evidence, and where there has been a history of so much fakery, chicanery and gullibility. With almost no evidence to constrain speculation, all things are possible.
For the anti-Bigfoot side, this means that there are no hard assertions against which to argue. Any legitimate objection will simply cause the pro-Bigfoot side to morph the proposal in order to evade the objection, something very easily done since there's no evidence to constraint speculation.
In other words, this discussion has to shift its focus somewhat in order to take on more of the character of a scientific discussion. Absence of evidence is not evidence of absence, and those arguing scientifically have to remember this rule. What can be done scientifically is to point out the paucity of evidence, and to put it in context by listing all the other speculated phenomena which have comparable amounts of evidence, e.g., UFO's, alien abductions, ghosts, ESP, pyramid power, magnetic bracelets, homeopathy, therapeutic touch, assisted communication, and so forth. Once that point has been made, then I think further discussion only leaves the realm of the scientific, with both the pro and anti sides taking advantage of the lack of evidence to engage in speculations about what is and isn't possible.
The pro-Bigfoot side has to keep in mind that the absence of contrary evidence doesn't mean something is real or possible. Science focuses on phenomena for which we have positive evidence, and once a hypothesis is formed it attempts to falsify the conclusions. The hypothesis most discussed in this thread is that there is a population of large primates living in the Pacific Northwest. Falsifying this hypothesis requires examining every inch of the Pacific Northwest, and so the hypothesis cannot in any practical sense be falsified. In other words, the hypothesis isn't scientific, and so there's no point arguing against it in the hope that is can be falsified. It simply isn't possible.
So I think the primary challenge is for the anti-Bigfoot side to try to put their position on a scientifically valid footing and avoid the pursuit of goals which aren't really scientifically possible.
--Percy