How does 客 (kè, "customer, guest") and 气 (qì, "gas, anger") combine to give 客气 （kèqi, "polite")? Looking up their definitions:


  客气 (kè qi) = polite
  客 (kè) = customer; visitor; guest
  气 (qì) = gas; air; smell; weather; vital breath; to anger; to get angry; to be enraged


There seems to be no logic behind combining 客 and 气 to give 客气.

Question: How does 客 and 气 combine to give 客气?
I think the logic is like 口气，语气. 

口气 is tone in English. 气 is air. 口气 is air from your mouth. Figuratively, it becomes your tone with which you speak. 

So, my thought for 客气 would be you speak in a guest's tone, which implies you are being polite.