The most common and most likely answer to this crossword clue is the 6 plus 5 letter word LADIES FIRST
I've seen this crossword clue in The Times
L
A
D
I
E
S
F
I
R
S
T
Buddy explains!
The straight part
We know that "what should he have said" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what should he have said = ladies first.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.