Adage Logic

The “internet logic” that a pyromancer should be able to hurt a fire elemental is that we’re made of meat and being punched hurts, so a being of flame that’s blasted by fire should be sore.

Of course, flame doesn’t have a lot of mass, nor will it impart a lot of kinetic force. The impact of a fiery explosion is mostly due to the shockwave and not the fire. So being hit by a fireball is less like being punched and more like a limp slap. And something more focused, like a scorching ray feels like it should have even less force behind it. 

This is ignoring the fact that two flames pass through each other with no resistance.