When I get to the insult sword-fighting stage of The Secret of Monkey Island, do I have to learn every single insult and comeback in order to beat the Sword Master?
Thankfully no, you don't have to learn them all. It is a bit tedious to get all the comebacks since some of the uncommon ones take a while to find.
To beat the Sword Master you only need to do comeback for a subset of all the insults, i.e. some of the Sword Master's insults have multiple comebacks. You can go to the Sword Master earlier but it requires some luck.
A defeated pirate will say "Wow! You're good enough to fight the Sword Master" once you have a good proportion of answers. I usually take this as the time I can go fight her:
If you don't know the answer to an insult from the Sword Master it isn't a real problem. You have a small margin of error before you are defeated... and I have never been given repeated insults in one fight so its not like she will continue to chain up the same insult in one single fight.
According to this source regarding insult responses:
There are 16 in all. Once you learn 12 and win three fights with normal pirates, they will begin to say 'You're good enough to fight the Sword Master'.