The cleanest historical answer is: “special” is a role, not a costume. Regular infantry exists to seize/hold ground and win by mass, endurance, and combined arms. Special forces exist to create outsized effects with small numbers—often by exploiting surprise, intelligence, and political/strategic leverage.
You can see this pattern back to ancient warfare (picked troops for raids, scouts, ambushes), but it becomes formalized in WWII: British Commandos (raids), SOE/OSS (sabotage, intelligence, resistance support), and long-range patrol groups (LRDG). Cold War doctrine then expands it: unconventional warfare, training partner forces, behind-the-lines reconnaissance, and counterinsurgency support—missions that don’t map neatly to “take hill, defend hill.”
Selection and training matter because these missions demand independent judgment, language/culture aptitude, and tolerance for uncertainty. But doctrine and command relationships matter just as much: SOF often report through different chains, get different authorities, and are tasked at higher levels where the political risk/benefit is calibrated. If you want a reading trail: US Army FM 3-05 (older editions), British commando history, and classic OSS/SOE accounts show why these units were built and why they stayed.