To “miss by a country mile” means you weren’t even as close as if you’d have only missed by a mile.
A country mile is an exaggeration of the 1,760 yards in the standardized English distance.
Rural roads in Britain twist and turn through the countryside.
So although the distance to be traveled is a mile, the real distance traveled on a winding road will be considerably greater than “as the crow flies,” or in a straight line.
That’s why a country mile is considered a greater distance than the average mile.