Why does Shanks sacrifice his arm to save Luffy? In Luffy's backstory, we saw that when Luffy was drowning and a Sea King attacks him, Shanks jumps in to save him and scares away the Sea King using Haki, losing an arm in the process. Why did he not use Haki to start with to chase away the Sea King, and thus, avoid losing his arm?
Okay, so as you know that Shanks was once a crew mate of Gol D Roger mentioned by Rayleigh himself when Luffy meets him. According to what was shown in flashback, Shanks tells Rayleigh about Luffy when he accidentally meets him on the Sabondy Archipelago.



Shanks had great respect towards Gol D Roger, and hearing the same words from Luffy and with the same enthusiasm, he could see a part of Roger in Luffy. The feeling what Shanks would have got can be proved by what was shown in Loguetown where Luffy said the same thing sitting in the bar. Even Raoul (the man who owns the bar) thought that Gol D Roger was back when he heard those words from Luffy. That could be one of the reasons.



Another reason is that he considered Luffy as a friend and he always said this:


  Listen up… You can pour drinks on me, you can throw food at me… You
  can even spit on me. I’ll just laugh that stuff off. But… Good reason
  or not… Nobody hurts a friend of mine.


So he could not withstand Luffy getting killed in front of his eyes.
This was the answer for your question in the heading.

Now the reason for not using haki was that Luffy is a hammer, hence cannot swim in water. Luffy was already drowning and it would be late if he went and used haki to send the sea king away and then go and save Luffy!