Peter Parker’s IQ is stated to be above 250, making him one of the smartest people on the planet. The web-shooters were part of Spider-Man’s original design and were used to demonstrate Peter’s intelligence. At the age of 15 he makes his own tech (such as: web fluid, the web-shooters, suit, utility belt). Where Peter doesn’t have an ability, he just makes himself a tool to fight crime. Over the years he has invented things such as: spider-traces, mini lie detectors, cryo cubes, multiple kinds of webbing and suits, stealth suit, spider-armor, Avengers identicards, Spider-Mobile, clean (almost limitless) power with endless applications (Parker Particles), Spider-Glider, Spider-Bots, and Webware.
On an interesting note, when Otto Octavius took over Peter’s body and life, he didn’t touch the web-shooters, only making the web fluid last longer in its solid state.