Why is pollution never a strictly local problem

Because there are many types of pollution. 
Air pollution, water pollution, etc.
The reason it is never local is because it's a chain reaction to the environment.
Example 1:
China has the worst air pollution in the world from factories and cars. The smoke has a depleting effect on the O-zone layer which protects humans from the sun's harmful UV rays. Also, without the protection of the o-zone layer, global warming is increased (yes, it's real) and glaciers begin to melt raising water levels and so forth. So even though the smoke is all the way in China, it affects all of us living on earth.
Example 2:
Let's say there is a oil spill in the ocean which potentially kills or endangers many organisms, like fish. Even though the oil spill was only in that part of the ocean, it affects all the animals because of something called the food chain. If all of a certain fish or animal dies out and that was another animals primary source of food, then it messes up the chain.