The question from the title is raised because in almost all introductory physics courses/textbooks the atmospheric pressure has been attributed to the weight of the column of air from a given level in the atmosphere up to its top. "Air is pressing on air." However the same textbooks, in the chapter on the kinetic theory of gases, tell students that a pressure in a gas enclosed in a container is due to variation of momentum suffered by the molecules, as a consequence of their impacts against the walls or against the surface of a test object placed inside the gas. The higher the number and average energy of molecules, the higher the pressure. Despite the fact that the atmosphere consists of matter that is mostly in the gas state, introductory physics textbooks do not justify why the concept of pressure from the kinetic theory of gases would not explain the physical nature of pressure in the atmosphere. Ricci-Torricelli's experiments realized by scientists from the Academia del Cimento suggest to abandon the "weight based" explanation in favor of a density-based explanation of atmospheric pressure. The dependence on altitude of air density, as well as of air pressure, is caused by Earth's gravitational force acting on all chaotically moving molecules in the atmosphere.