Consider the air elemental. It is made from air, or clouds, or smoke, or something like it. Any attempt to grab hold of such materials with your bare hands would fail, realistically speaking. Thus, barring the use of some very specific magic, one might presume that it is impossible to grapple an air elemental. Similar arguments would hold for fire and water elementals, for both fire and water cannot be gripped.
In D&D 5e, this is handled simply and directly by granting air, fire and water elementals immunity to the grappled condition.
In Pathfinder, however, I can find nothing indicating that these creatures are immune to being grappled. They usually have a solid bonus to Escape Artist checks, representing their slippery nature, but RAW anyone can grapple an air elemental as easily as a solid creature.
I note that the Pathfinder rules for grappling give both the grappler and the grapplee the grappled condition, so straight-up immunity to the grappled condition would complicate matters if the elemental were to attempt to grapple another creature (which is something these elementals could reasonably do). But hypothetically they could have been granted an ability similar to the freedom of movement spell, yet they were not.
Am I missing something? Is being able to grapple an air elemental a correct reading of Pathfinder's rules? Obviously, the DM has the freedom to rule as they deem fit, but if they decide to follow RAW how would one rationalise grappling something made of air?