Why did Shanks cut Kid's arm?
WTF IS HIS PROBLEM?
1. Shanks is an "arms dealer" or just likes to collect arms and may have taken Queen's in the past too?
2. Kid resembles Shanks sort of and Shanks took his arm as a moment of savage irony.
3. Shanks thought him too arrogant and wanted to humble him and show him how truly out of his depth he was and for probably understimating him too. A brutal, permanent lesson and reminder at that.
4. Shanks made him"bet that arm" in a similar way he bet his own arm on Luffy.
5. Kid might have openly declared he wants to kill Shanks and tried to attack him and since he uses his arms to attack, they cut him off his arm to "literally disarm him".
I think Kid has a personal reason to hate Shanks, some kind of vendetta, whether they are related or not. This article gives a great insight into the parallels and contrasts of Kid and Shanks, how they work as foils to one another despite their blatant similarities:
It makes me wonder if Oda is trying to do something similar with Bonney and Big Mom to think of it, despite Bonney's irrelevancy to Big Mom in the narrative so far ironically.