This is one of my favorite topics, and one of the few woo things that I actually ... well, don't believe in, but it could be possible. No supernatural, paranormal explanation required to explain bigfoot. If it exists, it's just a very, vary rare and elusive animal.
I really do think that the wooded areas of the Pacific Northwest are big enough that it is possible that there could be a large primate species hiding out there quite successfully. If you disagree, I would say that you probably don't have any idea how really BIG the uninhabited areas are out there. Kind of like creation science folk who don't believe in evolution because they just don't have any idea how really LONG five billion years is, and how many things can happen in that long of a period of time.
Finding bodies of animals is unusual in large wooded areas (thousands of square miles). Finding the body of a rare and maybe somewhat shy and intelligent animal would be even harder. Sure, I've found dead animals before in the woods, but not very often, and only of small rodents, of which there are many, and somewhat larger animals, like deer, of which there are also many.
But having said that, given that people have been reporting bigfoot for hundreds of years and we still haven't found a body ... and the times that people have seen it and had a camera and either got no photo or a very poor one, and the times when they had a rifle but just couldn't shoot it ... well, I can't calculate the odds, but it just seems very, very unlikely, making me fall on the side of thinking that it's more probable that bigfoot does not exist.
Possible .... sure. But possible doesn't means it's true. I just think that although it is possible, and would be a very exciting discovery if proven true, that the odds of bigfoot being real after all this time and all these sightings with no physical evidence resulting are very low.
Personally, if I had a gun and saw a bigfoot I can tell you the mystery would be solved that day. If you believe bigfoot exists, you probably think that it's very rare, and should be preserved and studied.
But it'll never happen. It probably just doesn't exist. Though it would be terribly interesting if it did.