Mostly because your mouths "wet", a ton of energy is required to heat or cool, water/saliva acts as thermal sink any hot soup or cold popsicles transfer energy only changes a few degrees and absorbs heat readily when changing state (ice/steam). If your mouth or tongue/gum skin were real dry it would be burned or freeze immediately instead. People with cavities, weak enamel, gum disease or Stomatitis are VERY hypersensitive to cold and heat in mouth is painful to them.

Conversely if you ran your hand under hot or cold water before touching something you'd be fine for a bit, is why wet newspaper is used for glassblowing, etc https://m.youtube.com/watch?v=eGqln2ZvTMQ