Why is the vac filtering flask, in the chem experiment, not connected directly to the vac?

I don't know what experiment you're talking about, but you generally want to have some kind of a liquid trap, such as an empty flask, in line between the vacuum source and your experiment. That way if you accidentally overfill your flask, the liquid will get sucked up and trapped in the second flask rather than getting sucked into the pump and corroding the motor.