Earth rotates from west to east causing the Sun, the Moon, stars and other planets rise from east and set in the west. On the surface of the earth each point is moving eastward with respect to an astronaut in space.
Thus if a rocket is launched at a small angle eastward vertically the speed of earth gets added to the rocket’s speed. This reduces the amount of fuel required. If the rocket is inclined along any other direction, the speed of the earth gets subtracted from the speed of rocket and will necessitate burning of more fuel.
In addition, in case of any failure during launch the rocket will fall back to the 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 concerns safety.