Why a space shuttle take off vertically?

Because if it took off horizontally, it would continue to circle the earth, hitting all those people in the boats that are watching the take-off, then continue until it came to a land mass and possibly strike buildings, vehicles, people...until it exploded into a fireball of great magnitude. So, to avoid this, NASA decided to have the shuttles take off vertically.

< It takes off vertically to reach less dense air ( less drag and aerodynamic heating ), and then begins a pitch maneuver to increase its tangential ( to the Earth) velocity; which eventually leads to a continuous orbit about the Earth. This procedure reduces the necessary on board mass of propellant on the spacecraft. The shuttle is essentially in free fall around the Earth ( imagine a cannon being fired at such a speed that it as it falls, the curvature of the Earth decreases in a proportional manner).>