Why do people only float in certain orientations? If the buoyant force on an object is equal to the weight of the water displaced by the object, why do people have an easier time floating on their back than vertically with their head sticking out of the water?
 A: The chest region provides the least dense region in the body since it traps a large airspace. And for either scenario (back floating or vertical) the chest is submerged.
So the only difference you need to consider is that in the vertical position, the head (at least above the nostrils) needs to be above the water line so that the person can breathe. But in the back floating position the nostrils can be positioned at the highest position, and thus more of the head , relative to the vertical position can be submerged - taking advantage of Archimedes's principle.
An adult human head weighs about 15 pounds so submerging as much of it as possible can eliminate the need to dog-paddle and thus passively maintain access for breathing.
Survival experts and SCUBA instructors will always train their pupils to float on their backs to conserve energy.
A: To answer the title: because there are two forces, weight and buoyant uplift, acting on the body and these act on the body at different points: the center of weight (and the center of bouyancy, respectively. Therefore, the pair will exert a torque on the body unless line joining them is aligned with the forces. So the body will come to rest with the center of buoyancy above the center of weight ("above" in the sense of being shallower in the water). The other equilibrium configuration is with the center of weight above the center of buoyancy, but this one is not stable in the sense that small perturbations on the body will cause the body to move away from this configuration.
So you will find it easiest to float in a configuration near to the stable equilibrium one. You can even stay in the unstable one with relatively little effort: you simply need to counteract perturbations with small swim thrusts to push you back to the unstable equilibrium configuration. To keep yourself in any other configuration, you need to be imparting a constant torque to yourself from swim thrusts to counteract the torque from the gravity-buoyancy couple.
When we say that a force like gravity or buoyancy acts at a point on a rigid body, what we mean is that the force comprises many contributions at different positions in the body. It can be shown that statics and dynamics of rigid bodies can be described by finding the point about which all the contributions have a torque of nought and thinking of the force system as a lone force acting at this zero torque point: it can be shown that the results of any analysis for a rigid body will be the same whether you use this method or analyse the whole system of forces. 
Weight is a sum of weight contributions from each part of your body. Buoyant uplift is a sum of pressures pushing on you at the surface of your body where it meets the water. So it should be clear that the zero torque points are in general very different for these forces.

Note: The center of weight is the same as a the center of mass in a uniform gravitational field.
