Why are satellites always launched from the east coast?

Earth rotates from west to east causing the sun, the moon, stars and other planets rise from the east and set in the west. On the surface of the earth each point is moving eastward with respect to an astronaut in a space. 

Thus if a rocket is launched at a small angle eastward vertically the speed of the earth is added to the speed of the rocket. This reduces the amount of fuel required. If the rocket is inclined along any other any direction, the speed of earth gets subtracted from the speed of the rocket and will necessitate burning of more fuel.

In addition, in case of any failure during the launch of the rocket will fall back to earth. Hence if it is launched from the east coast , the rocket will fall into the sea only. If it is launched from the west coast, in case of failure, the rocket will fall on the land endangering human habitats. Thus choosing eastward inclination is scientific but choice of eastern coast concern safety.