There are so many species in the world that man doesn't even know how many or cannot even count. Even at the rate of 11,000 a year going extinct (which, I don't see how that would even be possible to track, to be able to definitely say not a one of species XYZ exists anywhere in the world, especially when we are still discovering species unknown before, ones that did not just evolve), no one can make the claim that "most" species are on the verge of going extinct.
Not even close.
Extinction rates Future Biodiversity Threatened Fuzzy math extinction rates Unfortunately, now I must disagree with you. 
My current database is filled with articles such as these. I have linked them, but am unsure if everyone will be able to access them, as some require academic documentation. Sadly, Mass Extinction is not a query anymore, but a proven fact by many of the herpetologists around the world. Species are going extinct at a rate which might compare with the Tertiary and Triassic extinctions.
My understanding of the dwindling red squirrel numbers is that it is not for a lack of food. Rather, grey squirrels are doing *too* well because their resources are too plentiful and they are overwhelming the red squirrel (natural selection).
Although natural selection does indeed play its part, there is something much more sinister at work here: what is commonly called "squirrel pox". The grey squirrel is a carrier of this particular virus and it has developed antibodies to the disease. However the red squirrels have not, and usually succumb to this infection. The Institute of Zoology in the UK has found that the reds are in fact beginning to develop the beginnings of an antibody for this virus, and their "white papers" have been promising more assistance in the possibility of synthetic antibodies. Which would also benefit our reds over here across the pond.
I agree that squirrels are part of the food chain, and their population can get out of control if they are provided an unnatural abundance of resources. My backyard is an example of an overabundance of unnatural resources that I planted: tons of holly berries, hickory nuts and oak acorns, dogwood tree berries (I never have blooms thanks to the squirrels
) and on and on. The concentration of food in my yard would never occur in nature. And I do have a bird bath where all the squirrels rinse the nut shells out of their mouths, and I put fresh water in twice a day.
Wow...Your backyard sounds absolutely spectacular! Well....except for all the rabbit poop!
My poor Yorkies can't go in the backyard because the rabbit poop is unbelievably thick, and I recently learned that rabbit droppings can carry lepto. Max and Teddy never get to run off leash, as a result.
Not only rabbit droppings, but cats, foxes, mice, etc. In fact cats are carriers of Lepto, and as a carrier they show no symptoms of infection. However, their urine is loaded with bacteria.
I suppose if I had a backyard like yours, I would be upset if my pups could not even venture into it without fear of being accosted.
Aggression in squirrels and other animals can also be caused by humans feeding them, as was the case on my school campus. The squirrels were becoming so comfortable being around humans and receiving food, they started attacking for cheetos at lunchtime. The natural food sources on the campus were no longer satisfactory.