It started in the 60s in western movies, actually. At that time it was a product of camera framing - you could get a better view of the actors face and the gun in certain shots by holding the gun sideways.

It didn’t really explode culturally though until the sidegrip was featured in the opening of the film Menace II Society. That was what made holding your gun sideways the touchstone it is today.

The directors of that film saw a man use the sidegrip during a holdup in Detroit some years before. They used it in the film for all the reasons we still see it in culture today - it displays power, recklessness, and the dangerous, rough quality of somebody untrained in forearms using them with abandon. In short, it is visual display of the attitudes we typically see in “cool” characters.