It appears (as seems always seems to be the case) that we brought them on ourselves.
According to a recently-published paper, until the mid-1800s squirrels were not the prevalent force you see in cities and suburbs across the nation.
In 1847, Philadelphia released three squirrels in a park with food and shelter. Apparently the public thought these evil rodents were adorable. Then Frederick Law Olmsted designed his natural parks (Central Park in NYC) and introduced squirrels
as "possibly the only wildlife the [city] workers would ever see."
So remember, the next time one of the squirrel-Qaeda operatives takes all your birdseed, or chews through your telephone wire: they were put here for your entertainment. Are you entertained?