As ExtremeTech explained: "Stainless steel is much cheaper than carbon fiber, but it’s heavier. Although, Musk explains the rocket can be lighter with stainless steel than if you built it with other metals.
"Most steel alloys get brittle at cryogenic temperatures. That’s not the case for stainless steel with high chrome-nickel content. It gets stronger in cold conditions, but it also maintains ductility. That means stainless steel has high fracture toughness, which could prevent small structural imperfections from developing into cracks."