Why is the buoyant force on an object the net force instead of just the force pushing the object up? Why is the buoyant force on an object the net force (force pushing object up - force pushing object down) instead of just the force pushing the object up? Isn't the force pushing the object up what is really causing the buoyancy?
 A: Bouyant force is a direct effect of the pressure of a fluid on an object. The pressure pushes inward on the object everywhere on its surface. This means that the fluid is pushing downwards on the parts of the object's surface that are facing upward, and is pushing upwards on the parts of the object's surface that are facing downward (and, of course, is pushing horizontally on any vertical sides of the object). So yes, there is some component of the pressure that pushes downward on the object, and some component of the pressure that pushes upward.
The question then becomes: which component of the pressure is stronger? If the fluid pressure were perfectly uniform around the object, then neither would be stronger. But for any fluid in a gravitational field, the pressure increases with depth; for example, for nearly-incompressible fluids like water, $P=\rho g h$ for density $\rho$ and depth $h$. This means that the pressure on the bottom of the object is higher than the pressure on the top of the object, so the component of the pressure pushing upward is stronger than the component of the pressure pushing downward. So, when we add up all of the contributions of the pressure on the surface of the object, we find a net upward force. We call this net-upward force the buoyant force.
A: Your thinking is a little backwards. It's not like someone said, "I want to define something called the buoyant force, what should its definition be?". It just turns out that it is much more useful to talk about the net force exerted by the fluid than it is to just talk about the upward force from it. Hence we define the net force as the buoyant force.
If you want to split the buoyant force up into different parts, that's fine, but it doesn't mean the definition of the buoyant force is incorrect. You are just using a different definition.
