Why does Kirito hide his duel swords? On floor 74, Kirito hides his duel swords from Asuna and Clyde and then uses them at the last second. Why did he hide them?
He hid the skill to avoid the attention and envy of other players.


  Weapon skills that didn’t have clear conditions for appearing are
  called extra skills. They were sometimes even called random
  conditions. An example would be Klein’s «Katana». But «Katana»
  wasn’t all that rare and appeared quite often as long as you kept
  training the Curved Sword skill.
  Most of the ten-plus extra skills that had been found up until now,
  «Katana» included, had at least ten people who used each of them. The
  only exceptions were my «Dual Blades» and one other man’s extra skill.
  These two were most likely limited to only one person, so they
  should be called «Unique Skill». I had hidden the existence of my
  unique skill up until now. But from today, the news that I was the
  second unique skill user would spread throughout the world. There
  was no way I could hide it after using it in front of so many people.
  ...
  Since then, I only trained it when there was nobody around. Even
  after I nearly mastered it, I rarely used it against monsters unless it
  was an emergency. Aside from using it to protect myself in a crisis, I
  simply didn’t like this kind of skill due to the attention it draws.
  I even thought that it would be better if another Dual Blades user
  appeared-
  I scratched the area around my ear and muttered.
  “…if it became known that I had such a rare skill, not only would
  people pester me for information…it might attract other kinds of
  problems too…”
  Klein nodded.
  “Online gamers get jealous easily. I wouldn’t since I’m an
  understanding guy, but there sure are plenty of envious People.


As we can see later his fears were wellfounded:  


  Somehow they had found out about where I lived. As a result,
  swordsmen and information dealers had crowded around my house
  since early morning. I ended up having to go through the trouble of
  using a teleport crystal to escape.


Of note is that he wouldn't have hidden the skill if he had known how other players could unlock it.


  “I’m disappointed Kirito. You didn’t even tell me that you had
  such an awesome skill.”
  “I would have told you if I knew the conditions for its appearance.
  But I really couldn’t figure out how it happened.”
  I answered Klein’s complaint with a shrug.
  There wasn’t a shred of lie in what I said. About a year ago, I
  opened my skills window one day and found the name «Dual Blades»
  just sitting there. I really had no clue on what conditions made it
  appear.


The excerpts are from chapter 12 of the first light novel Aincrad (translations by Baka-Tsuki).